L. M. Fernández

L. M. Fernández
University of Seville | US · Departamento de Geometría y Topología

About

64
Publications
0
Reads
How we measure 'reads'
A 'read' is counted each time someone views a publication summary (such as the title, abstract, and list of authors), clicks on a figure, or views or downloads the full-text. Learn more
1,549
Citations

Publications

Publications (64)
Article
Full-text available
We study hypersurfaces isometrically immersed in a trans-S-manifolds in order to find out under what conditions they could inherit the structure of the ambient manifold and so, to obtain new examples of such trans-S-manifolds. Mainly, we investigate this situation depending the behaviour of the second fundamental form of the immersion.
Article
Full-text available
We present a new method to obtain a combinatorial representation for the behaviour of a submanifold isometrically immersed in a Riemannian manifold based on the second fundamental form. We also present several results applying this new way of representation.
Chapter
In this survey paper, we present a brief summary concerning the slant geometry for submanifolds in metric f-manifolds, together with some applications. The notion of f-structure was introduced by K.
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...
Article
In this paper, we establish some relationships between the main intrinsic invariants, scalar and Ricci curvatures, and the main extrinsic invariant, the mean curvature vector, for slant submanifolds of S-space-forms. In addition to that, we study those slant submanifolds satisfying the equality case between the above invariants, due to the great im...
Article
Full-text available
We prove that if the f-sectional curvature at any point of a ( 2 n + s ) -dimensional metric f-contact manifold satisfying the ( κ , μ ) nullity condition with n > 1 is independent of the f-section at the point, then it is constant on the manifold. Moreover, we also prove that a non-normal metric f-contact manifold satisfying the ( κ , μ ) nullity...
Preprint
Full-text available
We prove that if the $f$-sectional curvature at any point $p$ of a $(2n+s)$-dimensional $f$-$(\kappa,\mu)$ manifold with $n>1$ is independent of the $f$-section at $p$, then it is constant on the manifold. Moreover, we also prove that an $f$-$(\kappa,\mu)$ manifold which is not an $S$-manifold is of constant $f$-sectional curvature if and only if $...
Article
We consider generalized {(\kappa,\mu)} -paracontact metric manifolds satisfying certain flatness conditions on the {\mathcal{M}} -projective curvature tensor. Specifically, we study ξ- {\mathcal{M}} -projectively flat and {\mathcal{M}} -projectively flat generalized {(\kappa,\mu)} -paracontact metric manifolds and, further, ϕ- {\mathcal{M}} -projec...
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.
Preprint
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.
Chapter
In the present work, we briefly summarize our contributions to the study of CR submanifolds of (locally conformal almost) Kaehler manifolds and normal CR submanifolds of S-manifolds.
Article
We introduce para-S-manifolds and obtain some results concerning the curvature of these manifolds. In particular, we prove that there does not exist Einstein para-S-manifold, and consequently, we investigate \(\eta \)-Einstein para-S-manifolds and the conditions for them to be \(\xi \)-conformally flat.
Article
In this study, S-manifolds endowed with a semi-symmetric non-metric connection naturally related with the S-structure are considered and some general re-sults concerning the curvature of such connection are given. In particular, the con-ditions of semi-symmetry, Ricci semi-symmetry and projective semi-symmetry of this semi-symmetric non-metric conn...
Article
Full-text available
We establish some inequalities of Chen's type between certain intrinsic invariants (involving sectional, Ricci and scalar curvatures) and the squared mean curvature of submanifolds tangent to the structure vector fields of a generalized S-space-form and we discuss the equality cases of them. We apply the obtained results to slant submanifolds.
Article
We establish some inequalities of Chen's type between certain intrinsic invariants (involving sectional, Ricci and scalar curvatures) and the squared mean curvature of submanifolds tangent to the structure vector fields of a generalized S-space-form and we discuss the equality cases of them. We apply the obtained results to slant submanifolds.
Article
We investigate L-sectional curvature of S-manifolds with respect to the Rieman- nian connection and to certain semi-symmetric metric and non-metric connections naturally related with the structure, obtaining conditions for them to be constant and giving examples of S-manifolds in such conditions. Moreover, we calculate the scalar curvature in all t...
Article
In this study, S-manifolds endowed with a semi-symmetric metric connec-tion naturally related with the S-structure are considered and some curvature properties of such a connection are given. In particular, the conditions of semi-symmetry, Ricci semi-symmetry and Ricci-projective semi-symmetry of this semi-symmetric metric connection are investigat...
Article
Full-text available
We introduce and study generalized S-space-forms. Moreover, we investigate generalized S-space-forms endowed with an additional structure and we obtain some obstructions for them to be S-manifolds.
Article
We present a characterization theorem for the Maslov form in certain non-invari-ant slant submanifolds of S-space-forms to be closed and, from it, we deduce a topological obstruction for these types of non-invariant slant immersions. Moreover, we also give con-ditions for an anti-invariant submanifolds of an S-manifold, tangent to the structure vec...
Article
We define a new association between graphs and orthonormal bases of even-dimensional Euclidean vector spaces endowed with an special isomorphism motivated by the recently introduced theory of submanifolds associated with graphs. We provide several interesting examples and we analyze the shape of such graphs by proving some general results.
Article
We introduce and study generalized S-space-forms with two structure vector fields. We also present several examples of these manifolds such as certain hypersurfaces of Sasakianspace-forms, principal toroidal bundles and warped products. Moreover, we investigate generalized S-space-forms endowed with an additional structure and we obtain some obstru...
Article
This paper is focused on looking for links between the topology of a connected and non-compact surface with finitely many ends and any proper discrete Morse function which can be defined on it. More precisely, we study the non-compact surfaces which admit a proper discrete Morse function with a given number of critical elements. In particular, give...
Article
We characterize the topology of a graph in terms of the critical elements of a discrete Morse function defined on it. Besides, we study the structure and some properties of the gradient vector field induced by a discrete Morse function defined on a graph. Finally, we get results on the number of non-homologically equivalent excellent discrete Morse...
Article
We study non-anti-invariant slant submanifolds of generalized S-space-forms with two structure vector felds in order to know if they inherit the ambient structure. In this context, we focus on totally geodesic, totally umbilical, totally ƒ-geodesic and totally ƒ-umbilical non-anti-invariant slant submanifolds and obtain some obstructions. Moreover,...
Article
We get a characterization theorem for equivalent discrete Morse functions defined on simplicial complexes in terms of their gradient vector field. As a consequence, we also characterize them in the 1-dimensional case by using critical elements.
Article
Full-text available
The goal of this paper is to extend to infinite graphs the known Morse inequalities for discrete Morse functions proved by R. Forman [“Morse theory for cell complexes”, Adv. Math. 134, No. , 90–145 (1998; Zbl 0896.57023)] in the finite case. In order to get this result we shall use a special kind of infinite subgraphs on which a discrete Morse func...
Article
The goal of this work is to study the structure of the pure Morse complex of a graph, that is, the simplicial complex given by the set of all possible classes of discrete Morse functions (in Forman's sense) defined on it. First, we characterize the pure Morse complex of a tree and prove that it is collapsible. In order to study the general case, we...
Article
We study whether it is possible to obtain an induced structure on a slant submanifold of a metric f -manifold. Moreover, we give conditions for any isometric immersion between two metric f - manifolds to be slant and we prove a characterization theorem when the submanifold has the smallest possible dimension to be proper slant.
Article
Full-text available
The aim of this paper is to study the notion of critical element of a proper discrete Morse function defined on non-compact graphs and surfaces. It is an extension to the non-compact case of the concept of critical simplex which takes into account the monotonous behaviour of a function at the ends of a complex. We show how the number of critical el...
Article
Relationships between the Ricci curvature and the squared mean curvature and between the shape operator associated with the mean curva- ture vector and the sectional curvature function for slant submanifolds of an S-space-form are proved, particularizing them to invariant and anti-invariant submanifolds tangent to the structure vector flelds.
Article
Full-text available
Using the notion of discrete Morse function introduced by R. Forman for finite cw-complexes, we generalize it to the infinite 2-dimensional case in order to get the corresponding version of the well-known discrete Morse inequalities on a non-compact triangulated 2-manifold without boundary and with finite homology. We also extend them for the more...
Article
Relationships between the Ricci curvature and the squared mean curvature and between the shape operator associated with the mean curvature vector and the sectional curvature function for slant submani-folds of an S-space-form are proved, particularizing them to invariant and anti-invariant submanifolds tangent to the structure vector fields.
Article
A new class of Lie algebras of finite dimension, those which are associated with a certain combinatorial configuration made up by triangles of weighted and non-directed edges, is introduced and a characterization theorem for them is proved. Moreover, some subclasses of such Lie algebras are classified.
Article
Summary We study some special types of slant submanifolds of S-manifolds related to the second fundamental form of the immersion: totally f-geodesic and f-umbilical, pseudo-umbilical and austere submanifolds. We also give several examples of such submanifolds.
Article
Full-text available
We study slant submanifolds of $S$-manifolds with the smallest dimension, specially minimal submanifolds and establish some relations between them and anti-invariant submanifolds in $S$-manifolds, similar to those ones proved by B.-Y. Chen for slant surfaces and totally real surfaces in Kaehler manifolds.
Article
We study slant submanifolds of S-manifolds with the smallest di-mension, specially minimal submanifolds and establish some relations between them and anti-invariant submanifolds in S-manifolds, simi-lar to those ones proved by B.-Y. Chen for slant surfaces and totally real surfaces in Kaehler manifolds.
Article
Given a Lie algebra of finite dimension, with a selected basis of it, we show in this paper that it is possible to associate it with a combinatorial structure, of dimension 2, in general. In some particular cases, this structure is reduced to a weighted graph. We characterize such graphs, according to they have 3-cycles or not.
Article
Full-text available
We establish an interesting link between differential geometry and graph theory by defining submanifolds weakly associated with graphs. We prove that, in a local sense, every submanifold satisfies such an association, and other general results. Finally, we study submanifolds associated with graphs either in low dimensions or belonging to some speci...
Article
A version of Chen's inequality for a submanifold of an S-space-form, tangent to the structure vector fields of the ambient space, is established and some applications to the case of slant immersions are obtained from it. Proper slant submanifolds of minimum dimension satisfying the equality case are also characterized.
Article
We study the relationship between slant submanifolds in both Complex and Contact Geometry through Riemannian submersions. We present some construction procedures to obtain slant submanifolds in the unit sphere and in a Stiefel manifold. We also generalize them by means of the Boothby-Wang fibration. Finally, we show some characterization theorems o...
Article
Full-text available
We study the relationship between slant submanifolds in both Complex and Contact Geometry through Riemannian submersions. We present some construction procedures to obtain slant submanifolds in the unit sphere and in a Stiefel manifold. We also generalize them by means of the Boothby-Wang fibration. Finally, we show characterization theorems of thr...
Article
In this paper, we present the existence and uniqueness theorems for slant immersions into Sasakian-space-forms. By applying the first result, we prove several existence theorems for slant submanifolds. In particular, we prove the existence theorems for three-dimensional slant submanifolds with prescribed mean curvature or with prescribed scalar cur...
Article
Full-text available
In this paper, we study the possibility of obtaining an induced contact metric structure on a slant submanifold of a contact metric manifold. We also give a characterization theorem for three-dimensional slant submanifolds.
Article
Full-text available
In this paper, we show new results on slant submanifolds of an almost contact metric manifold. We study and characterize slant submanifolds of K-contact and Sasakian manifolds. We also study the special class of three-dimensional slant submanifolds. We give several examples of slant submanifolds.
Article
We present existence and uniqueness theorems for slant immersions into Sasakian-space-forms. By applying the first result, we prove several existence theorems for slant submanifolds. In particular, we prove existence theorems for three-dimensional slant submanifolds with prescribed mean curvature or with prescribed scalar curvature.
Article
Full-text available
We define and study both bi-slant and semi-slant submanifolds of an almost contact metric manifold and, in particular, of a Sasakian manifold. We prove a characterization theorem for semi-slant submanifolds and we obtain integrability conditions for the distributions which are involved in the definition of such submanifolds. We also study an intere...
Article
Full-text available
In this paper we study a class of K-contact manifolds, namely f-conformally flat K-contact manifolds and we show that a compact f-conformally flat K-contact manifold with regular contact vector field is a principal S1-bundle over an almost Kaehler space of constant holomorphic sectional curvature.
Article
Full-text available
In this paper, the notion of ξ-conformally flat on a contact metric structure is introduced and it is proved that any K-contact metric manifold is ξ-conformally flat if and only if it is an η-Einstein Sasakian manifold. Finally, some applications are given.
Article
In this paper, some properties of the geometry of pseudo-Einstein hypersurfaces of the S-manifold H2n+s are studied and a theorem concerning their principal curvatures is obtained.
Article
In this note a classification theorem for totally f-umbilical submanifolds of an S-space form is obtained.
Article
Full-text available
Cualquieralgebra de Lie de dimension Þnita, con una base Þ- jada, se puede asociar con una estructura combinatoria de dimension, en general, 2. En casos particulares, esta estructura es una conÞguracion plana y conexa de triangulos de aristas ponderadas y no dirigidas que, dos a dos, solo comparten un vertice o una arista. En este trabajo, se demue...

Network

Cited By