On the non-Riemannian quantity H of a Finsler metric ☆
On the non-Riemannian quantity H of a Finsler metric ☆
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DOI：
10.1016/j.difgeo.2008.06.002
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发表时间：
2009-02
影响因子：
0.5
通讯作者：
X. Mo
中科院分区：
文献类型：
--
作者：
X. Mo
芬斯勒几何的基本问题之一是在黎曼不变量和非黎曼不变量之间建立一些微妙的方程。受 Akbar-Zadeh 等结果的启发，本文在芬斯勒流形上的非黎曼量 H 和黎曼量之间建立了一个新的基本方程。作为其应用，我们证明所有 R 二次 Finsler 度量都具有消失的非黎曼不变 H 泛化结果，以前仅在 Randers 度量的情况下才知道。
One of fundamental problems in Finsler geometry is to establish some delicate equations between Riemannian invariants and non-Riemannian invariants. Inspired by results due to Akbar-Zadeh etc., this note establishes a new fundamental equation between non-Riemannian quantity H and Riemannian quantities on a Finsler manifold. As its application, we show that all R-quadratic Finsler metrics have vanishing non-Riemannian invariant H generalizing result previously only known in the case of Randers metric.