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Galaev S. V.

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

DOI
10.5922/0321-4796-2020-51-7
Pages
58-67
sub-Riemannian manifold of contact type interior connec­tion flat semi-metric connection with skew-symmetric torsion Schouten tensor

Abstract

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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