On semi-symmetric metric connection in sub-Riemannian manifold

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Published: Dec 30, 2016
DOI: https://doi.org/10.5556/j.tkjm.47.2016.1908
Keywords:
Sub-Riemmannian manifolds SS-connections Horizontal curvature tensors

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Yanling Han
Fengyun Fu
Peibiao Zhao

Abstract

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.

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How to Cite
Han, Y., Fu, F., & Zhao, P. (2016). On semi-symmetric metric connection in sub-Riemannian manifold. Tamkang Journal of Mathematics, 47(4), 373–384. https://doi.org/10.5556/j.tkjm.47.2016.1908
Issue
Vol. 47 No. 4 (2016)
Section
Papers
Author Biographies

Yanling Han

Department of AppliedMathematics, Nanjing University of Science and Technology, Nanjing 210094, P. R. China. School of Science, Qilu University of Technology, Jinan 250353, P. R. China.

Fengyun Fu

School ofMathematics and Statistics, Guangdong University of Finance and Economics, Guangzhou 510320, P. R. China.

Peibiao Zhao

Department of AppliedMathematics, Nanjing University of Science and Technology, Nanjing 210094, P. R. China.

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