Homogeneous Einstein -metrics on compact simple Lie groups and spheres

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• 作者：Zaili Yan^a ; ^{yanzaili@nbu.edu.cn" class="auth_mail" title="E-mail the corresponding author} ; Shaoqiang Deng^b ; ^{dengsq@nankai.edu.cn" class="auth_mail" title="E-mail the corresponding author}
• 关键词：53C21 ; 53C30 ; 53C60
• 刊名：Nonlinear Analysis
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：148
• 期：Complete
• 页码：147-160
• 全文大小：670 K

文摘

In this paper, we study homogeneous Einstein (α,β)$(\alpha ,\beta )$-metrics on compact Lie groups and spheres. We first show that any left invariant Einstein (α,β)$(\alpha ,\beta )$-metric on a connected compact simple Lie groups except $\mathrm{SU}\left(2\right)$ with vanishing S-curvature must be a Randers metric. Secondly, we prove that any c5dcab0fccc57c3880422a206572b28">$\mathrm{Sp}(n+1)$-invariant Einstein (α,β)$(\alpha ,\beta )$-metric on c6d1539830f07993f323b" title="Click to view the MathML source">S⁴ⁿ⁺³(n∈N⁺)$S^{4n+3}(n\in {\mathbb{N}}^{+})$ with vanishing S-curvature is either a Randers metric, or $\mathrm{SU}(2n+2)$-invariant. Finally, we give a complete description of $\mathrm{SU}(n+1)$-invariant Einstein Finsler metrics on c55a8c8341c0cc4436" title="Click to view the MathML source">S²ⁿ⁺¹(n≥2)$S^{2n+1}(n\ge 2)$.