Connections with parallel skew-symmetric torsion on sub-Riemannian manifolds
Year: 2020
Type: article
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.
Author: S. V. Galaev
Institution: Saratov State University
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W3082508354