Pablo Alegre

University of Seville | US

In this paper we study some curves of a trans-Sasakian manifold that generalize magnetic curves.

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.

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

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...

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...

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...

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...

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...

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.

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.

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.

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.

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.

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.

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.

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.

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...

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

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...

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...

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.

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...

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.

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.

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.