On the non-Riemannian quantity H of a Finsler metric

被引：26

作者：

Mo, Xiaohuan ^{[1
]}

机构：

[1] Peking Univ, Sch Math Sci, Key Lab Pure & Appl Math, Beijing 100871, Peoples R China

来源：

DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS | 2009年 / 27卷 / 01期

基金：

中国国家自然科学基金;

关键词：

Finsler manifold; Non Riemannian quantity H; R-quadratic metric; CONSTANT S-CURVATURE; FLAG CURVATURE; SCALAR CURVATURE; MANIFOLDS; SPACES;

D O I：

10.1016/j.difgeo.2008.06.002

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

One of fundamental problems in Finsler geometry is to establish some delicate equations between Riemannian invariants and non-Riemannian invariants. Inspired by results clue 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-quadrotic Finsler metrics have vanishing non-Riemannian invariant H generalizing result previously only known in the case of Randers metric. (C) 2008 Elsevier B.V. All rights reserved.

引用

页码：7 / 14

页数：8

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