A contact version of B.-Y. Chen's inequality and its applications to slant immersions

We establish a version of B.-Y. Chen’s inequality for a submanifold of a Sasakianspace-form, tangent to the structure vector field of the ambient space. We obtain some applications and we study this inequality for slant submanifolds. We also characterize 3–dimensional slant submanifolds satisfying the equality case.Plan Andaluz de Investigación (Junta de Andalucía

The curvature tensor of almost cosymplectic and almost Kenmotsu ( κ, μ, ν ) -space

We study the Riemann curvature tensor of (κ, µ, ν)-spaces when they have almost cosymplectic and almost Kenmotsu structures, giving its writing explicitly. This leads to the definition and study of a natural generalisation of the contact metric (κ, µ, ν)-spaces. We present examples or obstruction results of these spaces in all possible cases.Ministerio de Educación y Ciencia (MEC). EspañaPlan Andaluz de Investigación (Junta de Andalucía

Generalized (κ, µ)-space forms and d-homothetic deformations

We study the Da-homothetic deformations of generalized (κ, µ)- space forms. We prove that the deformed spaces are again generalized (κ, µ)-space forms in dimension 3, but not in general, although a slight change in their definition would make them so. We give infinitely many examples of generalized (κ, µ)-space forms of dimension 3

The curvature tensor of almost cosymplectic and almost Kenmotsu (κ,μ,ν)-spaces

We study the Riemann curvature tensor of (κ,μ, ν)-spaces when they have almost cosymplectic and almost Kenmotsu structures, giving its writing explicitly. This leads to the definition and study of a natural generalisation of the contact metric (κ,μ, ν)-spaces. We present examples or obstruction results of these spaces in all possible cases.Ministerio de Educación, Cultura y DeporteJunta de Andalucí

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

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

Graphs associated with vector spaces of even dimension: A link with differential geometry

AbstractWe 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

A classification of totally geodesic and totally umbilical Legendrian submanifolds of (κ, μ)-spaces

We present classifications of totally geodesic and totally umbilical Legendrian submanifolds of (κ, µ)-spaces with Boeckx invariant I ≤ −1. In particular, we prove that such submanifolds must be, up to local isometries, among the examples that we explicitly construct.Ministerio de Economía y CompetitividadFondo Europeo de Desarrollo RegionalPlan Andaluz de Investigación (Junta de Andalucía

Null pseudo-isotropic Lagrangian surfaces

In this paper we will show that a Lagrangian, Lorentzian surface M 2 1 in a complex pseudo space form Mf2 1 (4c) is pseudo-isotropic if and only if M is minimal. Next we will obtain a complete classification of all Lagrangian, Lorentzian surfaces which are lightlike pseudo-isotropic but not pseudo-isotropic.Ministerio de Economía y CompetitividadFondo Europeo de Desarrollo Regiona