A class of Einstein (α, β)-metrics

被引：0
|
作者：
Xinyue Cheng
Zhongmin Shen
Yanfang Tian
机构：
[1] Chongqing University of Technology,School of Mathematics and Statistics
[2] Indiana University-Purdue University at Indianapolis,Department of Mathematical Science
[3] Chongqing University of Technology,School of Mathematics and Statistics
[4] Logistical Engineering University of PLA,undefined
来源：
Israel Journal of Mathematics | 2012年 / 192卷
关键词：
Sectional Curvature; Ricci Curvature; Einstein Metrics; Riemann Curvature; Finsler Space;
D O I：
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中图分类号：
学科分类号：
摘要：
In this paper, we study a special class of Finsler metrics, called (α, β)-metrics, which are defined by F = αϕ(β/α), where α is a Riemannian metric and β is a 1-form. We show that if ϕ = ϕ(s) is a polynomial in s, it is Einstein if and only if it is Ricci-flat. We also determine the Ricci-flat (α, β)-metrics which are not of the type F = (α + ɛβ)2/α.
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页码：221 / 249
页数：28
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