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Homogeneous Einstein Manifolds with Vanishing $S$ Curvature

Published online by Cambridge University Press:  22 February 2019

Libing Huang
Affiliation:
School of Mathematical Sciences and LPMC, Nankai University, Tianjin 300071, P. R. China Email: [email protected]
Zhongmin Shen
Affiliation:
Department of Mathematical Sciences, Indiana University-Purdue University, Indianapolis, IN 46202-3216, USA Email: [email protected]
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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.

Type
Article
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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