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

doi:10.1007/s11464-016-0614-z

Front. Math. China

2017, Vol. 12

Issue (2) : 417-439 https://doi.org/10.1007/s11464-016-0614-z

RESEARCH ARTICLE

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

Hongchuan XIA¹(

),Chunping ZHONG²

¹. College of Mathematics and Statistics, Xinyang Normal University, Xinyang 464000, China
². School of Mathematical Sciences, Xiamen University, Xiamen 361005, China

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Abstract

Let (M,F) be a Finsler manifold, and let TM₀ 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 (TM₀,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.

Keywords Finsler manifold foliation constant flag curvature Vaisman connection

Corresponding Author(s): Hongchuan XIA

Issue Date: 27 December 2016

Cite this article:

Hongchuan XIA,Chunping ZHONG. A class of metrics and foliations on tangent bundle of Finsler manifolds[J]. Front. Math. China, 2017, 12(2): 417-439.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-016-0614-z
https://academic.hep.com.cn/fmc/EN/Y2017/V12/I2/417

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