Einstein Finsler metrics and Killing vector fields on Riemannian manifolds

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 S^3 with Ric = 2F^2, Ric = 0 and Ric =-2F^2, respectively. This family of metrics...

Full description

Saved in:
Bibliographic Details
Published inScience China. Mathematics Vol. 60; no. 1; pp. 83 - 98
Main Authors Cheng, XinYue, Shen, ZhongMin
Format Journal Article
LanguageEnglish
Published Beijing Science China Press 2017
Springer Nature B.V
Subjects
Applications of Mathematics
Brownian motion
Curvature
Fields (mathematics)
Finsler度量
Killing型
Mathematics
Mathematics and Statistics
Riemann manifold
Riemann流形
向量场
度量和
旗曲率
爱因斯坦
黎曼流形
Einstein metric
53B40
(a, ß)-metric
Killing vector field
Ricci curvature
Finsler metric
53C60
Ricci-flat metric
Online AccessGet full text

Cover

More Information
Summary: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 S^3 with Ric = 2F^2, Ric = 0 and Ric =-2F^2, 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.
Bibliography: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 S^3 with Ric = 2F^2, Ric = 0 and Ric =-2F^2, 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.
Killing vector field Finsler metric （α,β）-metric Ricci curvature Einstein metric Ricci-flat metric
11-5837/O1
ISSN:1674-7283
1869-1862
DOI:10.1007/s11425-016-0303-6