A class of Einstein (α, β)-metrics

被引：30
|
作者：
Cheng, Xinyue [1 ]
Shen, Zhongmin [2 ]
Tian, Yanfang [1 ,3 ]
机构：
[1] Chongqing Univ Technol, Sch Math & Stat, Chongqing 400054, Peoples R China
[2] Indiana Univ Purdue Univ, Dept Math Sci, Indianapolis, IN 46202 USA
[3] Logist Engn Univ PLA, Chongqing 400016, Peoples R China
来源：
ISRAEL JOURNAL OF MATHEMATICS | 2012年 / 192卷 / 01期
关键词：
Sectional Curvature; Ricci Curvature; Einstein Metrics; Riemann Curvature; Finsler Space;
D O I：
10.1007/s11856-012-0036-x
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we study a special class of Finsler metrics, called (alpha, beta)-metrics, which are defined by F = alpha I center dot(beta/alpha), where alpha is a Riemannian metric and beta is a 1-form. We show that if I center dot = I center dot(s) is a polynomial in s, it is Einstein if and only if it is Ricci-flat. We also determine the Ricci-flat (alpha, beta)-metrics which are not of the type F = (alpha + E >beta)(2)/alpha.
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页码：221 / 249
页数：29
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