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

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.

Keywords

• sub-riemannian manifold of contact type
• interior connection
• flat semi-metric connection with skew-symmetric torsion
• schouten tensor