Beldjilali Gherici

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• Professor
• Professor at University Mustapha Stambouli of Mascara

Motivated by the recent studies of C_12-manifolds, which are non-normal almost contact metric manifolds, in this article we investigate the magnetic curves with respect to contact magnetic fields in C 12-manifolds. Moreover, some properties of twin magnetic curves are investigated. Finally, some examples are presented.

These papers include a set of exercises with detailed solutions on the following topics: Mathematical logic, sets and functions, binary relations, algebraic structures and the polynomial ring. This work is directed to first year university students.

Polynomials are very simple objects but with extremely rich properties. You already know how to solve equations of degree 2. Did you know that the resolution of equations of degree 3, was the subject of fierce struggles in Italy in the 16-th century?. A competition was organized with a prize for each of thirty equations of degree 3 to be solved. A...

The investigation of Yamabe solitons within almost contact metric manifolds has garnered significant interest recently, producing notable findings. This paper aims to explore the inverse problem: constructing almost contact metric structures on a three-dimensional Riemannian manifold endowed with an almost Yamabe soliton. Subsequently, we provide t...

This chapter is concerned with studying algebraic structures for first-year university students (Algebra 1). It includes three parts, the first on groups, the second on the ring and the third on the field in addition to examples and exercises.

Relations in a set is the third chapter in the Algebra 1 scale. It includes the concepts of equivalence relations and order relations with properties, illustrative examples, as well as exercises for understanding and training.

This chapter includes various definitions and properties related to sets and functions, with illustrative examples and exercises for practice.

This is the first chapter of scale: Algebra 1, for students of the first year Mathematics in university of Mascara (Algeria) which includes the following topics: 1) Proposition and Compound proposition, 2) Quantifiers, 3) Types of Mathematical Proofs, with examples and exercises.

In this paper, we construct almost contact metric structures on a three-dimensional Riemannian manifold equipped with an almost Ricci soliton. Then, we give the techniques necessary to define the nature of such structures. Concrete examples are given.

The present paper is devoted to a class of manifolds which admit an f-structure with 2-dimensional parallelizable kernel. Such manifolds are called 4-dimensional almost bi-contact metric manifolds; they carry a locally conformal almost Kähler structure. We give some classifications and prove their fundamental properties, then we deduce some propert...

The present paper is devoted to three-dimensional C_12-manifolds (defined by D. Chinea and C. Gonzalez), which are never normal. We study their fundamental properties and give concrete examples. As an application, we study such structures on three-dimensional Lie groups.

Motivated by the recent studies of the harmonic maps on normal almost contact metric manifolds, in particular Sasakian, Kenmotsu, and cosymplectic manifolds, in this article we investigate the harmonic maps on C 12-manifolds which are non-normal almost contact metric manifolds. Finally, some examples are presented.

The present paper is devoted to 4-dimentional Hermitain manifold. We give a new necessary and sufficient condition of integrability and we introduce a new class of locally conformal K\"ahler manifolds that we consider a twin of the Vaisman ones. Then, some basic properties of this class is discussed, also the existence of such manifolds is shown wi...

The object of this article is to study a new class of almost contact metric structures which are integrable but non normal. Secondly, we explain a method of construction for normal manifold starting from a non-normal but integrable manifold. Illustrative examples are given.

The purpose of this paper is to construct families of Sasakian structures and Kenmotsu structures on the product of a single Sasakian manifold with an orientable surface. Concrete examples are given. 2000 Mathematics Subject Classification. 53C25, 53D17.

We study almost contact metric structures on 3-dimensional Lie algebras and investigate the class of left invariant almost contact metric structures on the corresponding Lie groups. We introduce a general approach and we obtain a full classification in dimension three.

The aim of this paper is two-fold. First, a new characterization of any three-dimensional almost contact metric structure is obtained. Second, the necessary and sufficient condition for these structures to be integrable is determined, and an equivalent condition is given in terms of ∇ξ. Illustrative examples are given.

The aim of this paper is two-fold. First, the study of $C_{12}$-structure (called by us corner structure) is extended to the general case without any condition, unlike our previous papers (see, \cite{BB, BG2, BG, BBB}). Second, starting from a $C_{12}$-structure which is not normal, we construct Trans-Sasakian structures which are normal. Class of...

The aim of this paper is twofold. First, we study the Chinea-Gonzalez class C_12 of almost contact metric manifolds and we discuss some fundamental properties. We show there is a one-to-one correspondence between C_12 and Kählerian structures. Secondly, we give some basic results for Riemannian curvature ten-sor of C_12-manifolds and then establish...

In this paper, we investigate the behavior of Ricci solitons under Generalized $\mathcal{D}$-conformal deformation on cosymplectic manifolds. We derive expressions for the deformation tensor and explore the changes that occur to the soliton vector field and the soliton constant under deformation. Our results reveal interesting insights into the beh...

In this article, we investigate the behavior of Ricci solitons under D-isometric deformations on a class of Riemannian manifolds. A D-isometry is a diffeomorphism that preserves the distance function induced by a Riemannian metric up to a constant factor. We consider a family of Riemannian metrics g on a manifold M that are related by D-isometric d...

The object of this article is to study a new class of almost contact metric structures which are integrable but non normal. Illustrativeexamples are given. Mathematics Subject Classification (2010). Primary 53C15; Secondary 53C55.

The object of this article is to study a new class of almost con- tact metric structures which are integrable but non normal. Secondly, a method of construction for normal manifold starting from a non-normal but integrable manifold. Illustrative examples are given. Mathematics Subject Classification (2010). Primary 53C15; Secondary 53C55.

The purpose of this paper is to introduce a new class of locally conformal Kähler manifolds which will generalize the Vaisman manifold. Then, some basic properties of this class is discussed, also the existence of such manifolds is shown with concrete examples. As an application, we study such structures on four-dimensional solvable Lie algebra.

Legendre curves play a very important and special role in geometry and topology of almost contact manifolds.There are certain results known for Legendre curves in 3-dimensional normal almost contact manifolds. The aim of this paper is to study Legendre curves of three-dimensional $C_{12}$-manifolds which are non-normal almost contact manifolds and...

في هذا الكتاب سنتناول البنية المترية التلامسية تقريبا و البنى التلامسية على المنوّعات الريمانية ذات البُعد الفردي، ندرس أهم الخواص مع براهين مفصّلة و أمثلة توضيحية تمهيدا للفصل الأساسي الموالي و الذي يحوي دراسة مفصّلة عن البُنى المترية التلامسية تقريباً ثلاثية الأبعاد مع استعراض لأصنافها الخمسة حسب تصنيف تشينيا-غونزليز. نشير أنه من بين الأصناف الخم...

Legendre curves play a very important and special role in geometry and topology of almost contact manifolds.There are certain results known for Legendre curves in 3-dimensional normal almost contact manifolds. The aim of this paper is to study Legendre curves of three-dimensional $C_{12}$-manifolds which are non-normal almost contact manifolds and...

The purpose of the present paper is to introduce a new class of almost para-contact metric manifolds namely, Golden para-contact metric manifolds. Then, we are particularly interested in a more special type called Golden para-Sasakian manifolds, where we will study their fundamental properties and we present many examples which justify their study.

This note provides a quite obvious observation that the condition (2.7), which is a part of the original definition of the so-called para-Kenmotsu manifolds [9], does not make sense, and thus this concept is void. So, it is proved that the para-Kenmotsu manifolds does not exist under the condition mentioned above.

Slant curves and in particular Legendre curves play a very im-1 portant and special role in geometry and topology of almost contact man-2 ifolds. There are certain results known for these curves in 3-dimensional 3 normal almost contact metric manifolds. In the presented paper, we 4 study the slant curves in the case of 3-dimensional non-normal almo...

In the present paper we study 3-dimensional C 12-manifolds ad-1 mitting Ricci solitons and generalized Ricci solitons and then we introduce 2 a new generalization of η-Ricci soliton. We give a class of examples. 3 M.S.C. 2010: 42A20, 42A32. 4

In the present paper, we introduce a new class of structures on an even dimensional differentiable Riemannian manifold which combines, well known in literature, the Sasakian and Kenmotsu structures simultaneously. The structure will be called a Sasaki–Kenmotsu structure by us. Firstly, we discuss the normality of the Sasaki–Kenmotsu structure and g...

In this note, we find a necessary condition on odd-dimensional Riemannian manifolds under which both of Sasakian structure and the generalised Ricci soliton equation are satisfied, and we give some examples.

In this paper, we introduce a new class of Kählerian manifolds and study their essential examples as well as their fundamental properties. Next, we investigate a particular type belonging to this class and we establish some basic results for Riemannian curvature tensor. Concrete examples are given.

In this note, we find a necessary condition on odd-dimensional Riemannian manifolds under which both of Sasakian structure and the generalised Ricci soliton equation are satisfied, and we give some examples.

The object of the present paper is to introduce a new transformation of almost contact metric manifolds. Firstly, starting from a Sasakian manifold we construct another Sasakian manifold and we prove some geometric properties. Secondly, we study Ricci solitons in Sasakian manifolds under this deformation. Concrete examples are given. 2000 Mathemati...

In this article, we study some properties of three dimensional \(C_{12}\)-manifolds and we give a method of construction for normal manifold starting from a non-normal but integrable manifold. Concrete examples are given.

In this article, we study some properties of three dimensional C12-manifolds and we give a method of construction for normal manifold starting from a non-normal but integrable manifold. Concrete examples are given. Mathematics Subject Classification. Primary 53C15; Secondary 53C55.

In this work, we have investigated a new deformation of almost contact metric manifolds. New relations between classes of 3-dimensional almost contact metric have been discovered. Several concrete examples are discussed.

وُضِع هذا الكتاب ليكون موافقا لمتطلبات البرنامج الخاص بمقياس المنحنيات و السطوح المقرّر لطلبة السنة الأولى ماستر رياضيات تخصّص هندسة. هذا المرجع يضم دراسة مستفيضة للمنحنيات والسطوح الكائنة في الفضاء الإقليدي ثلاثي الأبعاد، دراسة خارجية نظرا لضرورة وجود فضاء حاو للعناصر الهندسية قيد الدراسة من منحنيات أو أسطح و دراسة ذاتية من خلال التحكّم في الخواص...

إعتمادا على البحث الذي نشر مؤخرا للدكاترة ح. بوزير، غ .بلجيلالي وب. بيور، عَملنا على دراسة المنوّعة المترية التلامسية تقريبا الجديدة التي وردت في البحث المشار إليه بتفصيل يجعل قارئ هذه المذكرة يستوعب هذا النوع من المنوّعات مع تدعيم الدراسة بأمثلة ملموسة و مفصلة. وفي الختام قدّ منا دراسة جديدة و أصيلة عن كيفية إنشاء هذه البنى على جبور ليي بعتبارها م...

In this paper, we discuss some geometric properties of almost complex Golden structure (i.e. a polynomial structure with the structure polynomial Q(X) = X 2 −X + 3 2 I) and we introduce such some new classes of almost Hermitian Golden structures. We give a concrete examples. M.S.C. 2010: 53B35, 53C15, 53C55, 53D15, 53C25.

امتدادا ً للورقة البحثية التي قدمها الدكتور بلجيلالي غريسي، عملنا في هذه المذكّرة على دراسة البنية المترية التلامسية تقريبا ًعلى المنوّعة القابلة للتوازي ، وخصصنا زمر ليي بذلك باعتبارها منوّعة قابلة للتوازي

It’s shown that for some changes of metrics and structural tensors, the product of two transSasakian manifolds is a Kählerian manifold. This gives new positive answer and more generally to Blair-Oubina’s open question. (See [7] and [17]). Concrete examples are given.

It’s shown that for some changes of metrics and structural tensors, the product of two transSasakian manifolds is a Kählerian manifold. This gives new positive answer and more generally to Blair-Oubina’s open question. Concrete examples are given.

We introduce the notion of D-isometric warping and we use it to construct a 1-parameter family of Kahlerian structures from a single Sasakian structure and also a quaternionic Kahlerian structure from a Sasakian 3-structure.

In this paper, we introduce a new class of almost Golden Riemannian structures and study their essential examples as well as their fundamental properties. Next, we investigate a particular type belonging to this class and we establish some basic results for Riemannian curvature tensor and the sectional curvature. Concrete examples are given.

In this work, we have dealt with almost contact metric structures induced by Golden structures and simultaneously as one can be obtained from the other, and provided the following results besides some side ones. Various examples are discussed.

In this paper, we construct a Sasakian manifold by the product of real line and Kählerian manifold with exact Kähler form. This result demonstrates the close relation between Sasakian and Kählerian manifold with exact Kähler form. We present an example and an open problem.

Affine connections compatible with a contact structure are defined and conditions for two compatible connections on a Sasaki manifold to form a dualistic structure are given.

In this paper, starting from only a global basis of vector fields, we construct a class of almost contact metric manifolds and we give concrete example. Next, we study some essential types belonging to this class on dimension 3 and we construct several examples.

We establish an interesting class of almost Golden Riemannian manifolds such as the s-Golden manifolds and we construct a concrete example.Then, we give a more special type in this class.

In this paper, we introduce a new class of almost Golden Riemannian manifolds and we construct a concrete example. Then, we are particularly interested in two more special types where we will study their fundamental properties and we present many examples which justify their study... To read this article, click on the following link: https://rdcu...

The notion of Golden manifold M was defined by Crasmareanu and Hretecanu in [2] by a tensor field Φ on M satisfying Φ 2 = Φ+I where I is the identity transformation. The authors studied some properties of this manifold and they have showed that Φ is an automorphism of the tangent bundle TM and its eigenvalues are = and  * =1-. There are also sev...

في هذا العرض، سنوضّح إحدى الطرق الجميلة و غير المستعملة عموما في حساب موتّر التقوّس الريماني. تعتمد هذه الطريقة على الصيغ التفاضلية الأحادية و الثنائية .لذا، وَجَب الإلمام بها قبل قراءة هذه الأوراق.

In this paper we give a generalization of the doubly D-homothetically warped metric introduced by Blair [4], and we study the construction of Kahlerian structure on the product of two almost contact metric structures. It is shown that if one factor is β-Kenmotsu, the other is β-Kenmotsu or α-Sasakian, and if one factor is cosymplectic, the other is...

The aim of this paper is to construct a 1-parameter family of Sasakian manifold starting from a single Sasakian manifold. Concrete examples are given.

In this work, we have dealt with almost contact metric structures induced by Golden structures and simultaneously as one can be obtained from the other, and provided the following results besides some side ones. Various examples are discussed.

هدف مذكرتنا هذه هو دراسة نوع جديد من البنى الهجينة التي تتمتع بخواص البنية الريمانية الذهبية تقريبا و البنية المترية التلامسية تقريبا في آن واحد و اقتصرنا في دراستنا هذه على المنوّعات ثلاثية الأبعاد. * و نشير الى أن هذا العمل يعتبر أول مذكرة ماستر في الرياضيات تقدم باللغة الوطنية ( العربية ) على الأقل في جامعة معسكر.

We introduce the notion of Golden Riemannian manifolds of type (r, s) and starting from a Golden Riemannian structure, we construct some remarkable classes of the induced structures on Riemannian manifold. Concret examples are given. .... Sorry, I am unable to share my full-text because I don't know if I have permission to me. But you can find it...

Polycopi de Cours Structure complexe. Ce cours est destiné aux étudiants en première année master spécialité mathématiques option géométrie différentielle et applications. Dans ce polycopie sont donns quelques bases sur les variétés complexe, les variétés hermitiennes, les variétés Kählrienne et les différentes relations entre eux.

In this paper, we construct a Sasakian structure on the product of Sasakian manifold and Kählerian manifold with exact Kähler form.

The purpose of this paper is to determine some remarkable classes of the induced structures on the product of a locally conformally Kähler manifold with the real line and an almost contact metric manifold.

The metric called D-homothetic bi-warping that we introduced on the product of a Riemannian manifold with an almost contact metric manifold as a generalization of warped product and D-homothetic warping allows us to construct: - A family of Kählerian structures starting from a Sasakian manifold. - A 1-parameter family of conformal Kähler structures...

The aim of this paper is two-fold. First, new generalized Kähler manifolds are constructed starting from both classical almost contact metric and almost Kählerian manifolds. Second, the transformation construction on classical Riemannian manifolds is extended to the generalized geometry setting.

The aim of this paper is two-fold. First, new generalized Kähler manifolds are constructed starting from both classical almost contact metric and almost Kählerian manifolds. Second, the transformation construction on classical Riemannian manifolds is extended to the generalized geometry setting.

The purpose of this paper is to define some classes of almost contact metric 3-structures manifolds and almost quaternionic metric with an almost Hermitian almost contact metric structure. Next, we construct an almost quaternionic Hermitian structure on the product of two almost Hermitian almost contact metric structures. This gives a new positive...

We introduce the notion of D-homothetic bi-warping and starting from a Sasakian manifold M , we construct a family of Kählerian structures on the product R × M. After, we investigate conditions on the product of a cosymplectic or Kenmotsu manifold and the real line to be a family of conformal Kähler manifolds. We construct several examples. MSC : 5...

We introduce the notion of D-homothetic bi-warping and starting from a Sasakian manifold M , we construct a family of Kählerian structures on the product R × M. After, we investigate conditions on the product of a cosymplectic or Kenmotsu manifold and the real line to be a family of conformal Kähler manifolds. We construct several examples. MSC : 5...

The purpose of this paper is to define some classes of almost contact metric 3-structures manifolds and almost quaternionic metric with an almost Hermitian almost contact metric structure. Next, we construct an almost quaternionic Hermitian structure on the product of two almost Hermitian almost contact metric structures. This gives a new positive...

We study the Bochner pseudosymmetry, Weyl pseudosymmetry and holo-morphic projective pseudosymetry conditions for¨Kahlerianfor¨ for¨Kahlerian mani-folds and we show that are not essential in dimension greater than 4. For a 4-dimensional, many interesting relations between the various pseudosymmetry conditions of¨Kahlerian of¨ of¨Kahlerian manifolds...

In the present paper, we prove that for a 4-dimensional properly pseudosymmetric Kählerian manifold M, the Ricci tensor vanishes on the set p Î {M/ f(p) 6≠ 0} where f is the structure function (i.e R(X,Y ) = f(XÙY).R) and for f > 0 the manifold is not compact. Various examples are discussed.

Dans ce mémoire, on a étudie la semi-symétrie et la pseudo-symétrie d’une variété Käehlérienne et leurs interprétation géométriques, en suite l’étude de La pseudo-symétrie holomorphique pour les variétés Käehlériennes et les variétés Kählériennes à courbures sectionnelle quasi-constante holomorphique (ou variété Kählérienne QCH).

هذا العرض خاص بمناقشة مذكرة الماجيستير، و هو يتعلق بدراسة شبه التناظر على منوّعات كالير.