On conformally flat (α,β)-metrics with relatively isotropic mean Landsberg curvature

被引：9

作者：

Cheng, Xinyue ^{[1
]}

Li, Haixia ^{[1
]}

Zou, Yangyang ^{[1
,2
]}

机构：

[1] Chongqing Univ Technol, Sch Math & Stat, Chongqing 400054, Peoples R China

[2] Southwest Univ, Sch Math & Stat, Chongqing 400715, Peoples R China

来源：

PUBLICATIONES MATHEMATICAE-DEBRECEN | 2014年 / 85卷 / 1-2期

基金：

中国国家自然科学基金;

关键词：

(alpha; beta)-metric; conformally flat Finsler metric; mean Landsberg curvature; weak Landsberg metric; METRICS;

D O I：

10.5486/PMD.2014.5863

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we study conformally flat (alpha, beta)-metrics in the form of F = alpha phi(beta/alpha), where alpha is a Riemannian metric and beta is a 1-form on the manifold. We prove that conformally flat weak Landsberg (alpha, beta)-metrics must be either Riemannian metrics or locally Minkowski metrics. Further, we prove that, if phi(s) is a polynomial in s, then conformally flat (alpha, beta)-metrics with relatively isotropic mean Landsberg curvature must also be either Riemannian metrics or locally Minkowski metrics.

引用

页码：131 / 144

页数：14

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