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

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• 作者：Hongchuan Xia ; Chunping Zhong
• 关键词：Finsler manifold ; foliation ; constant flag curvature ; Vaisman connection
• 刊名：Frontiers of Mathematics in China
• 出版年：2017
• 出版时间：April 2017
• 年：2017
• 卷：12
• 期：2
• 页码：417-439
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics, general;
• 出版者：Higher Education Press
• ISSN：1673-3576
• 卷排序：12

文摘

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.