Differential geometry on complex and almost complex spaces

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

Sasaki-like almost contact complex Riemannian manifolds

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

A connection with parallel torsion on almost hypercomplex manifolds with Hermitian and anti-Hermitian metrics

Conformally invariant tensors on almost contact manifolds with b-metric

Almost hypercomplex pseudo-Hermitian manifolds are considered. Isotropic hyper-Kahler manifolds are introduced. A 4-parametric family of 4-dimensional manifolds of this type is constructed on a Lie group. This family is characterized geometrically. The condition a 4-manifold to be isotropic hyper-Kahler is given.

Almost hypercomplex pseudo-Hermitian manifolds and a 4-dimensional Lie group with such 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 subject of investigations are the almost hypercomplex manifolds with Hermitian and anti-Hermitian (Norden) metrics. A linear connection D is introduced such that the structure of these manifolds is parallel with respect to D and its torsion is totally skew-symmetric. The class of the nearly Kahler manifolds with respect to the first almost complex structure is of special interest. It is proved that D has a D-parallel torsion and is weak if it is not flat. Some curvature properties of these manifolds are studied.

A connection with parallel totally skew-symmetric torsion on a class of almost hypercomplex manifolds with hermitian and anti-hermitian metrics

The subject of investigations are the almost hypercomplex manifolds with Hermitian and anti-Hermitian (Norden) metrics. A linear connection D is introduced such that the structure of these manifolds is parallel with respect to D and its torsion is totally skew-symmetric. The class of the nearly Kaehler manifolds with respect to the first almost complex structure is of special interest. It is proved that D has a D-parallel torsion and is weak if it is not flat. Some curvature properties of these manifolds are studied.

Kostadin Gribachev

Papers

Conformally invariant tensors on almost contact manifolds with b-metric

Almost hypercomplex pseudo-Hermitian manifolds and a 4-dimensional Lie group with such structure

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

A connection with parallel totally skew-symmetric torsion on a class of almost hypercomplex manifolds with hermitian and anti-hermitian metrics

A connection with parallel totally skew-symmetric torsion on a class of almost hypercomplex manifolds with Hermitian and anti-Hermitian metrics