Homogeneous Einstein (α, β)-metrics on compact simple Lie groups and spheres. (January 2017)

• Record Type: Journal Article
• Authors: Yan, Zaili; Deng, Shaoqiang
• Is Part Of: Nonlinear analysis. Volume 148(2017)
• Page Start: 147
• Page End: 160
• Publication Date: 2017-01
• Subjects: 53C21 -- 53C30 -- 53C60; Finsler space -- (α, β)-metric -- Einstein (α, β)-metric; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2016.09.016
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: In this paper, we study homogeneous Einstein ( α, β ) -metrics on compact Lie groups and spheres. We first show that any left invariant Einstein ( α, β ) -metric on a connected compact simple Lie groups except SU ( 2 ) with vanishing S-curvature must be a Randers metric. Secondly, we prove that any Sp ( n + 1 ) -invariant Einstein ( α, β ) -metric on S 4 n + 3 ( n ∈ N + ) with vanishing S-curvature is either a Randers metric, or SU ( 2 n + 2 ) -invariant. Finally, we give a complete description of SU ( n + 1 ) -invariant Einstein Finsler metrics on S 2 n + 1 ( n ≥ 2 ) .