Einstein Finsler metrics and killing vector fields on Riemannian manifolds

被引：0
|
作者：
XinYue Cheng
ZhongMin Shen
机构：
[1] Chongqing University of Technology,School of Mathematics and Statistics
[2] Indiana University-Purdue University,Department of Mathematical Sciences
来源：
Science China Mathematics | 2017年 / 60卷
关键词：
Killing vector field; Finsler metric; (a, ß)-metric; Ricci curvature; Einstein metric; Ricci-flat metric; 53B40; 53C60;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We use a Killing form on a Riemannian manifold to construct a class of Finsler metrics. We find equations that characterize Einstein metrics among this class. In particular, we construct a family of Einstein metrics on S3 with Ric = 2F2, Ric = 0 and Ric = -2F2, respectively. This family of metrics provides an important class of Finsler metrics in dimension three, whose Ricci curvature is a constant, but the flag curvature is not.
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页码：83 / 98
页数：15
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