A classification of the torsion tensors on almost contact manifolds with B-metric

Abstract

The space of the torsion (0,3)-tensors of the linear connections on almost contact manifolds with B-metric is decomposed in 15 orthogonal and invariant subspaces with respect to the action of the structure group. Three known connections, preserving the structure, are characterized regarding this classification.

17 pages, exposition clarified, references added

References in corpus (8)

• On the classification of the almost contact metric manifolds
• Canonical-type connection on almost contact manifolds with B-metric
• A connection with skew symmetric torsion and Kähler curvature tensor on quasi-Kähler manifolds with Norden metric
• A natural connection on some classes of almost contact manifolds with B-metric
• Natural Connections on Riemannian Product Manifolds
• Almost Paracontact Manifolds
• Natural connections on conformal Riemannian P-manifolds
• Linear Connections on Normal Almost Contact Manifolds with Norden Metric

Cited by in corpus (10)

• Sasaki-like almost contact complex Riemannian manifolds
• Lie groups as 3-dimensional almost contact B-metric manifolds
• A natural connection 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
• 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