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

Abstract

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.

17 pages

References in corpus (9)

• Twisting Hermitian and hypercomplex geometries
• A connection with parallel torsion on 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
• Almost hypercomplex pseudo-Hermitian manifolds and a 4-dimensional Lie group with such structure
• A connection with skew symmetric torsion and Kähler curvature tensor on quasi-Kähler manifolds with Norden metric
• On hypercomplex pseudo-Hermitian manifolds
• On the geometry of the connection with totally skew-symmetric torsion on almost complex manifolds with Norden metric
• Connection with parallel totally skew-symmetric torsion on almost complex manifolds with Norden metric
• Some four-dimensional almost hypercomplex pseudo-Hermitian manifolds

Cited by in corpus (21)

• Sasaki-like almost contact complex Riemannian manifolds
• Lie groups as 3-dimensional almost contact B-metric manifolds
• A connection with parallel totally skew-symmetric torsion on a class of almost hypercomplex manifolds with Hermitian and anti-Hermitian metrics
• A classification of the torsion tensors on almost contact manifolds with B-metric
• Canonical-type connection on almost contact manifolds with B-metric
• A natural connection on some classes of almost contact manifolds with B-metric
• Curvature properties on some classes of almost contact manifolds with B-metric
• Pair of associated Schouten-van Kampen connections adapted to an almost contact B-metric structure
• On canonical-type connections on almost contact complex Riemannian manifolds
• The moduli space of Type~A surfaces with torsion and non-singular symmetric Ricci tensor
• On Geometry of Manifolds with Some Tensor Structures and Metrics of Norden Type
• Almost contact B-metric manifolds with curvature tensors of Kähler type
• Moduli spaces of oriented Type A manifolds of dimension at least 3
• Natural Connections with Totally Skew-Symmetric Torsion on Manifolds with Almost Contact 3-Structure and Metrics of Hermitian-Norden Type
• Space-like and time-like hyperspheres in real pseudo-Riemannian 4-spaces with almost contact B-metric structures
• Lie groups as 3-dimensional almost contact B-metric manifolds in the main vertical classes
• Natural connections with torsion expressed by the metric tensors on almost contact manifolds with B-metric
• Lie groups as 3-dimensional almost contact B-metric manifolds in two main classes
• Moduli spaces of Type~$\mathcal{B}$ surfaces with torsion
• On some Lie groups as 5-dimensional almost contact B-metric manifolds with three natural connections
• Almost contact B-metric manifolds as extensions of a 2-dimensional space-form