Abstract
Let (M,F) be a Finsler manifold, and let TM 0 be the slit tangent bundle of M with a generalized Riemannian metric G, which is induced by F. In this paper, we extract many natural foliations of (TM 0,G) and study their geometric properties. Next, we use this approach to obtain new characterizations of Finsler manifolds with positive constant flag curvature. We also investigate the relations between Levi-Civita connection, Cartan connection, Vaisman connection, vertical foliation, and Reinhart spaces.
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Acknowledgements
This work was supported by the National Natural Science Foundation of China (Grant Nos. 11271304, 11671330, 11571288) and the Nanhu Scholars Program for Young Scholars of Xinyang Normal University.
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Xia, H., Zhong, C. A class of metrics and foliations on tangent bundle of Finsler manifolds. Front. Math. China 12, 417–439 (2017). https://doi.org/10.1007/s11464-016-0614-z
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DOI: https://doi.org/10.1007/s11464-016-0614-z