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A classification of the torsion tensors on almost contact manifolds with B-metric. (English) Zbl 1310.53069

The authors state a classification of the torsion tensors of type \((0,3)\) on an almost contact manifold with a B-metric. They prove that the space of these tensors is decomposed in 15 orthogonal and invariant subspaces with respect to the action of the structure group. Also, they find characterizations of some well-known natural connections via their classification theorem.

MSC:

53D15 Almost contact and almost symplectic manifolds
53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.)
53C05 Connections (general theory)
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