Tamkang University, Tamkang Journal of Mathematics, 4(47), p. 373-384, 2016
DOI: 10.5556/j.tkjm.47.2016.1908
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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.