ALMOST CONTACT B-METRIC MANIFOLDS WITH CURVATURE TENSORS OF KÄHLER TYPE (original) (raw)

Curvature tensors on some five-dimensional almost contact B-metric manifolds

There are considered 5-dimensional almost contact B-metric manifolds of two basic classes. It is proved that every manifold from the section of these classes is with pointwise constant sectional curvatures. It is studied the curvature tensor of the manifolds of these two classes and some their curvature characteristics are given.

Canonical-type connection on almost contact manifolds with B-metric

Annals of Global Analysis and Geometry, 2012

The canonical-type connection on the almost contact manifolds with B-metric is constructed. It is proved that its torsion is invariant with respect to a subgroup of the general conformal transformations of the almost contact B-metric structure. The basic classes of the considered manifolds are characterized in terms of the torsion of the canonical-type connection.

Curvature properties on some classes of almost contact manifolds with B-metric

Comptes Rendus De L Academie Bulgare Des Sciences Sciences Mathematiques Et Naturelles, 2011

Almost contact manifolds with B-metric are considered. Of special interest are the so-called vertical classes of the almost contact B-metric manifolds. Curvature properties of these manifolds are studied. An example of 5-dimensional manifolds is constructed and characterized.

Almost contact structures and curvature tensors

Kodai Mathematical Journal, 1981

We determine an orthogonal decomposition of the vector space of some curvature tensors on a co-Hermitian real vector space, in irreducible components with respect to the natural induced representation of c U(n)xl.

The curvature tensor of (\ka,\mu,\nu)-contact metric manifolds

2011

We study the Riemann curvature tensor of (\kappa,\mu,\nu)-contact metric manifolds, which we prove to be completely determined in dimension 3, and we observe how it is affected by D_a-homothetic deformations. This prompts the definition and study of generalized (\kappa,\mu,\nu)-space forms and of the necessary and sufficient conditions for them to be conformally flat.

The curvature tensor of (κ,μ,ν)-contact metric manifolds

2015

We study the Riemann curvature tensor of (κ, µ, ν)-contact metric manifolds, which we prove to be completely determined in dimension 3, and we observe how it is affected by Da-homothetic deformations. This prompts the definition and study of generalized (κ, µ, ν)-space forms and of the necessary and sufficient conditions for them to be conformally flat.Ministerio de Educación y CienciaFondo Europeo de Desarrollo RegionalPlan Andaluz de Investigación (Junta de Andalucía

Curvature properties on some three-dimensional almost contact manifolds with B-metric, II

The curvature tensor on a 3-dimensional almost contact manifold with B-metric belonging to two main classes is studied. These classes are the rest of the main classes which were not considered in the first part of this work. The dimension 3 is the lowest possible dimension for the almost contact manifolds with B-metric. The corresponding curvatures are found and the respective geometric characteristics of the considered manifolds are given.