Differential Geometry of Manifolds

2020 №51

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Connections with parallel skew-symmetric torsion on sub-Riemannian manifolds



On a sub-Riemannian manifold M of contact type, is considered an N-connection  defined by the pair (, N), where  is an interior metric connection,  is an endomorphism of the distribution D. It is proved that there exists a unique N-connection  such that its torsion is skew-symmetric as a contravariant tensor field. A construction of the endomorphism corresponding to such connection is found. The sufficient conditions for the obtained connection to be a metric connec­tion with parallel torsion are given.


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