Open AccessOn semi-symmetric metric connection in sub-Riemannian manifold
Author(s) -
Yazhou Han,
Fengyun Fu,
Peibiao Zhao
Publication year - 2016
Publication title -
tamkang journal of mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.324
H-Index - 18
eISSN - 0049-2930
pISSN - 2073-9826
DOI - 10.5556/j.tkjm.47.2016.1908
Subject(s) - mathematics , levi civita connection , connection (principal bundle) , fundamental theorem of riemannian geometry , metric connection , pseudo riemannian manifold , pure mathematics , riemannian manifold , manifold (fluid mechanics) , statistical manifold , metric (unit) , mathematical analysis , ricci curvature , information geometry , geometry , scalar curvature , curvature , mechanical engineering , operations management , economics , engineering
The authors firstly in this paper define a semi-symmetric metric non-holonomic connection (in briefly, SS-connection) on sub-Riemannian manifolds. An invariant under a SS-connection transformation is obtained. The authors then further give a result that a sub-Riemannian manifold $(M,V_{0},g,\bar{\nabla})$ is locally horizontally flat if and only if $M$ is horizontally conformally flat and horizontally Ricci flat.