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A class of non-holonomic projective connections on sub-Riemannian manifolds

Han Yanling (Nanjing University of Science and Technology, Department of Applied Mathematics, Nanjing, P.R. China + Qilu University of Technology, School of Science, Jinan, P.R. China)
Fu Fengyun (Guangdong University of Finance and Economics, School of Mathematics and Statistics, Guangzhou, P.R. China)
Zhao Peibiao (Nanjing University of Science and Technology, Department of Applied Mathematics, Nanjing, P.R. China)

The authors define a semi-symmetric non-holonomic (SSNH)-projective connection on sub-Riemannian manifolds and find an invariant of the SSNH-projective transformation. The authors further derive that a sub-Riemannian manifold is of projective flat if and only if the Schouten curvature tensor of a special SSNH-connection is zero.

Keywords: Sub-Riemannian manifolds, Non-holonomic connection, SSNH-projective connection