A class of metrics and foliations on tangent bundle of Finsler manifolds  

作　　者：Hongchuan XIA Chunping ZHONG 

机构地区：[1]College of Mathematics and Statistics, Xinyang Normal University, Xinyang 464000, China [2]School of Mathematical Sciences, Xiamen University, Xiamen 361005, China

出　　处：《Frontiers of Mathematics in China》2017年第2期417-439,共23页中国高等学校学术文摘·数学（英文）

基　　金：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.

摘　　要：Let （M, F） be a Finsler manifold, and let TMo 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 （TMo, 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.Let （M, F） be a Finsler manifold, and let TMo 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 （TMo, 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.

关 键 词：Finsler manifold FOLIATION constant flag curvature Vaismanconnection 

分 类 号：O186.14[理学—数学] O186.1[理学—基础数学]