Pablo Alegre

Pablo Alegre
Universidad Pablo de Olavide | UPO · Statistics

About

21
Publications
3,670
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718
Citations
Citations since 2017
8 Research Items
415 Citations
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2017201820192020202120222023020406080100
2017201820192020202120222023020406080100
2017201820192020202120222023020406080100

Publications

Publications (21)
Article
Full-text available
Recently, trans- S -manifolds have been defined as a wide class of metric f -manifolds which includes, for instance, f -Kenmotsu manifolds, S -manifolds and C -manifolds and generalize well-studied trans-Sasakian manifolds. The definition of trans- S -manifolds is formulated using the covariant derivative of the tensor f and although this formulati...
Chapter
In [11], Chen introduced slant submanifolds of an almost Hermitian manifold, as those submanifolds for which the angle between JX and the tangent space is constant, for any tangent vector field X. These submanifolds play an intermediate role between complex submanifolds and totally real ones.2000 Mathematics Subject Classification.53C1553C2553C4053...
Chapter
Slant submanifolds were defined in the nineties by B.-Y. Chen and the corresponding theory has had an increasing development.2000 AMS Mathematics Subject Classification53C4053C4253C50
Article
Full-text available
In this paper, we introduce the notion of ∗\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$*$$\end{document}-slant submanifold as that slant submanifold whose second fu...
Article
Full-text available
The Maslov form is a closed form for a Lagrangian submanifold of C m , and it is a conformal form if and only if M satisfies the equality case of a natural inequality between the norm of the mean curvature and the scalar curvature, and it happens if and only if the second fundamental form satisfies a certain relation. In a previous paper we present...
Article
Full-text available
In this paper, we introduce the notion of bi-slant submanifolds of a para Hermitian manifold. They naturally englobe CR, semi-slant, and hemi-slant submanifolds. We study their first properties and present a whole gallery of examples.
Preprint
In this paper we introduce the notion of bi-slant submanifolds of a para Hermitian manifold. They naturally englobe CR, semi-slant and hemi-slant submanifolds. We study their first properties and present a whole gallery of examples.
Article
Full-text available
In this paper, we introduce the notion of slant submanifolds of a para-Hermitian manifold. We study their first properties and present a whole gallery of examples.
Article
Full-text available
We introduce a new general class of metric f-manifolds which we call (nearly) trans-S-manifolds and includes S- manifolds, C-manifolds, s-th Sasakian manifolds and generalized Kenmotsu manifold studied previously. We prove their main properties and we present many examples which justify their study.
Article
In this paper, we extend the notion of generalized Sasakian space form to the semi-Riemannian setting. We consider several interesting cases and we give examples of them all. We also study their structures.
Article
In this paper we introduce the notion of slant submanifolds of a Lorentzian almost contact manifold and of a Lorentzian almost para contact mani-fold.
Article
Full-text available
In this study, we establish a sharp relation between δ-invariants and Riemannian submersions with totally geodesic fibers. By using this relationship, we establish an optimal inequality involving δ-invariants for submanifolds of the complex projective space CP m (4) via Hopf’s fibration ${\pi:S^{2m+1}\to CP^{m}(4)}$ . Moreover, we completely clas...
Article
Full-text available
In this paper we introduce the notion of semi-invariant submanifolds of a Lorentzian almost contact manifold. We study their principal characteristics and the particular cases in which the manifold is a Lorentzian Sasakian manifold or a Lorentzian Sasakian space form.
Article
The study of generalized Sasakian space forms is continued in this paper. The behavior of such spaces under generalized D-conformal deformations is analyzed. As a consequence, new examples of generalized Sasakian space forms are given. Mathematics Subject Classification (2010)Primary 53C25–Secondary 53D15
Article
Full-text available
In this study we consider the focal curve Cγ of a space curve γ and its focal curvatures. We characterize some special types of ruled surface, choosing one of the base curves or director curves as the focal curve of the space curve γ. Finally we construct new types of ruled surface and calculate their distinguished parameters. We give necessary and...
Article
In this study we consider the focal curve C γ of a space curve γ and its focal curvatures. We characterize some special types of ruled surface, choosing one of the base curves or director curves as the focal curve of the space curve γ. Finally we construct new types of ruled surface and calculate their distinguished parameters. We give necessary an...
Article
In the present paper submanifolds of generalized Sasakian-space-forms are studied. We focus on almost semi-invariant submanifolds, these generalize invariant, anti-invariant, and slant submanifolds. Sectional curva-tures, Ricci tensor and scalar curvature are also studied. The paper finishes with some results about totally umbilical submanifolds.
Article
This paper is about the talk given in the VIth Geometry Sympo- sium in Bursa, Turkey, on July 2008. We present the notion of CR-submanifolds of a Lorentzian almost contact manifold, study their principal characteristics and the particular cases in which the manifold is a Lorentzian Sasakian mani- fold or a Lorentzian Sasakian space form. We also pr...
Article
In this paper, contact metric and trans-Sasakian generalized Sasakian-space-forms are deeply studied. We present some general results for manifolds with dimension greater than or equal to 5, and we also pay a special attention to the 3-dimensional cases.
Article
In this article, we investigate sharp inequalities involving δ-invariants for submanifolds in both generalized complex space forms and generalized Sasakian space forms, with arbitrary codimension.
Article
Full-text available
Generalized Sasakian-space-forms are introduced and studied. Many examples of these manifolds are presented, by using some different geometric techniques such as Riemannian submersions, warped products or conformal and related transformations. New results on generalized complex-space-forms are also obtained.

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