Open AccessConnections with parallel skew-symmetric torsion on sub-Riemannian manifolds
Author(s) -
S. V. Galaev
Publication year - 2020
Publication title -
differencialʹnaâ geometriâ mnogoobrazij figur
Language(s) - English
Resource type - Journals
eISSN - 2782-3229
pISSN - 0321-4796
DOI - 10.5922/0321-4796-2020-51-7
Subject(s) - levi civita connection , mathematics , endomorphism , connection (principal bundle) , covariance and contravariance of vectors , metric connection , pure mathematics , torsion (gastropod) , parallel transport , fundamental theorem of riemannian geometry , christoffel symbols , mathematical analysis , manifold (fluid mechanics) , ricci curvature , geometry , curvature , medicine , mechanical engineering , surgery , engineering
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.