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Homogeneous Einstein Finsler Metrics on $(4n+3)$-dimensional Spheres

Part of: Local differential geometry Global differential geometry

Published online by Cambridge University Press:  09 November 2018

Libing Huang  and
Xiaohuan Mo
Libing Huang
Affiliation:
School of Mathematical Sciences, Nankai University, Tianjin 300071, China Email: huanglb@nankai.edu.cn
Xiaohuan Mo
Affiliation:
Key Laboratory of Pure and Applied Mathematics, School of Mathematical Sciences, Peking University, Beijing 100871, China Email: moxh@pku.edu.cn
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Abstract

In this paper, we study a class of homogeneous Finsler metrics of vanishing $S$-curvature on a $(4n+3)$-dimensional sphere. We find a second order ordinary differential equation that characterizes Einstein metrics with constant Ricci curvature $1$ in this class. Using this equation we show that there are infinitely many homogeneous Einstein metrics on $S^{4n+3}$ of constant Ricci curvature $1$ and vanishing $S$-curvature. They contain the canonical metric on $S^{4n+3}$ of constant sectional curvature $1$ and the Einstein metric of non-constant sectional curvature given by Jensen in 1973.

Keywords

Finsler metrichomogeneous spaceEinstein metric

MSC classification

Primary: 53B40: Finsler spaces and generalizations (areal metrics)
Secondary: 53C60: Finsler spaces and generalizations (areal metrics)
Type
Article
Information
Canadian Mathematical Bulletin , Volume 62 , Issue 3 , September 2019 , pp. 509 - 523
Copyright
© Canadian Mathematical Society 2018 

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Footnotes

Author Mo is the corresponding author. Author Huang was supported by the National Natural Science Foundation of China 11301283 and 11571185. Mo was supported by the National Natural Science Foundation of China 11771020.

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