Differential geometry on complex and almost complex spaces

Structures on Manifolds

A natural connection with totally skew-symmetric torsion on almost contact manifolds with B-metric is constructed. The class of these manifolds, where the considered connection exists, is determined. Some curvature properties for this connection, when the corresponding curvature tensor has the properties of the curvature tensor for the Levi-Civita connection and the torsion tensor is parallel, are obtained.

Natural connection with totally skew-symmetric torsion on almost contact manifolds with b-metric

Natural connection with totally skew-symmetric torsion on almost contact manifolds with B-metric

The object of investigations are almost contact B-metric structures on 3-dimensional Lie groups considered as smooth manifolds. There are established the existence and some geometric characteristics of these manifolds in all basic classes. An example is given as a support of obtained results.

Lie groups as 3-dimensional almost contact B-metric manifolds

The class of the Riemannian almost product manifolds with nonintegrable structure is considered. Some identities for curvature tensor as certain invariant tensors and quantities are obtained.

On Riemannian almost Product Manifolds with Nonintegrable Structure

A 4-parametric family of 4-dimensional quasi-Kahler manifolds with Norden metric is constructed on a Lie group. This family is characterized geometrically. The condition for such a 4-manifold to be isotropic Kahler is given.

A lie group as a 4-dimensional quasi-k¨ ahler manifold with norden metric

The basic class of the non-integrable almost complex manifolds with Norden metric is considered. Its curvature properties are studied. The isotropic Kaehler type of investigated manifolds is introduced and characterized geometrically.

Dimitar Mekerov

Papers

Lie groups as 3-dimensional almost contact B-metric manifolds

On Riemannian almost Product Manifolds with Nonintegrable Structure

A lie group as a 4-dimensional quasi-k¨ ahler manifold with norden metric

On the geometry of quasi-Kaehler manifolds with Norden metric

On Lie groups as quasi-Kähler manifolds with Killing Norden metric