Submanifolds of generalized Sasakian space forms

In the present paper submanifolds of generalized Sasakian-spaceforms are studied. We focus on almost semi-invariant submanifolds, these generalize invariant, anti-invariant, and slant submanifolds. Sectional curvatures, Ricci tensor and scalar curvature are also studied. The paper finishes with some results about totally umbilical submanifolds.Plan Andaluz de Investigación (Junta de Andalucía)Ministerio de Educación y CienciaFondo Europeo de Desarrollo Regiona

Bi-slant submanifolds of para Hermitian manifolds

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.Ministerio de Economía y Competitividad (MINECO). EspañaEuropean Commission (EC). Fondo Europeo de Desarrollo Regional (FEDER)Plan Andaluz de Investigación, Desarrollo e Innovación (PAIDI)Instituto de Matemáticas de la Universidad de Sevilla (IMUS

On generalized Sasakian-space-forms

We study contact metric and trans-Sasakian generalized Sasakian-space-forms. We also give some interesting examples of generalized Sasakian-space-forms by using warped products and conformal changes of metric.Ministerio de Educación y CienciaFondo Europeo de Desarrollo RegionalPlan Andaluz de Investigación (Junta de Andalucía)Korea Research Foundatio

A closed form for slant submanifolds of generalized Sasakian space forms

The Maslov form is a closed form for a Lagrangian submanifold of Cm, 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 presented a natural inequality between the norm of the mean curvature and the scalar curvature of slant submanifolds of generalized Sasakian space forms, characterizing the equality case by certain expression of the second fundamental form. In this paper, first, we present an adapted form for slant submanifolds of a generalized Sasakian space form, similar to the Maslov form, that is always closed. And, in the equality case, we studied under which circumstances the given closed form is also conformal.Junta de AndalucíaMinisterio de Economía y Competitividad (MINECO). Españ

New examples of generalized Sasakian-space-forms

In this paper we study when a non-anti-invariant slant submanifold of a generalized Sasakian-space-form inherits such a structure, on the assumption that it is totally geodesic, totally umbilical, totally contact geodesic or totally contact umbilical. We obtain some general results (including some obstructions) and we also offer some explicit examples.Plan Andaluz de Investigación (Junta de Andalucía)Ministerio de Economía y Competitivida

Some special types of developable ruled surface

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 sufficient conditions for these types of ruled surface to become developable

B.-Y. Chen's inequality for submanifolds of generalized space forms

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.Ministerio de Educación y CienciaPlan Andaluz de Investigación (Junta de Andalucía

Subvariedades en espacios de curvatura Ø-seccional constante generalizados

La curvatura de Riemann es una importante herramienta en el estudio de variedades. Así, es de sobra conocida la clasificación de los espacios de curvatura constante en función del valor de dicha curvatura. En Geometría Compleja, F. Tricerri y L. Vanhecke ampliaron este estudio a los espacios de curvatura seccional holomorfa constate generalizados. En esta tesis, se intr oduce el caso análogo en Geometría Casi-Contacto, definiendo los espacios de curvatura Ø-seccional constante generalizados. Se presentan interesantes ejemplos y estudiamos sus propiedades fundamentales. En la segunda parte se realiza un estudio de las desigualdades de B.-Y. Chen para subvariedades de un espacio de curvatura Ø-seccional constante generalizado

Can trans-S-manifolds be defined from the Gray-Hervella classification for almost Hermitian manifolds?

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 formulation coincides with the characterization of trans-Sasakian manifolds in such a particular case, this latter type of manifolds were not initially defined in this way but using the Gray-Hervella classification of almost Hermitian manifolds. The aim of this paper is to study how (almost) trans-S-manifolds relate with the Gray-Hervella classification and to establish both similarities and differences with the trans-Sasakian case