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Homogeneous Einstein Manifolds with Vanishing $S$ Curvature

Part of: Global differential geometry

Published online by Cambridge University Press:  22 February 2019

Libing Huang  and
Zhongmin Shen
Libing Huang
Affiliation:
School of Mathematical Sciences and LPMC, Nankai University, Tianjin 300071, P. R. China Email: huanglb@nankai.edu.cn
Zhongmin Shen
Affiliation:
Department of Mathematical Sciences, Indiana University-Purdue University, Indianapolis, IN 46202-3216, USA Email: zshen@math.iupui.edu
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Abstract

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Infinitely many new Einstein Finsler metrics are constructed on several homogeneous spaces. By imposing certain conditions on the homogeneous spaces, it is shown that the Ricci constant condition becomes an ordinary differential equation. The regular solutions of this equation lead to a two parameter family of Einstein Finsler metrics with vanishing $S$ curvature.

Keywords

homogeneous Finsler spaceEinstein manifoldS curvature

MSC classification

Primary: 53C30: Homogeneous manifolds
Secondary: 53C60: Finsler spaces and generalizations (areal metrics)

Information

Type
Article
Information
Canadian Mathematical Bulletin , Volume 62 , Issue 3 , September 2019 , pp. 525 - 537
Copyright
© Canadian Mathematical Society 2019 

Footnotes

The first author is supported by NSFC Grant (no. 11301283, 11571185) and the Fundamental Research Funds for the Central Universities. The second author is supported by NSFC Grant (no. 11671352). This work was done during the first author’s visit to IUPUI.

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