2014/01/02 by Ming Xu, Xu, Ming, Shaoqiang Deng +1
Mathematics · Physics and Astronomy · #22E46 #53C30 #Advanced Algebra and Geometry #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Finite Group Theory Research
paper · doi:10.48550/arxiv.1401.0472
openalex publication_date 2014/01/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we introduce a new type of Finsler metrics, called (α1,α2)-metrics. We define the notion of the good datum of a homogeneous (α1,α2)-metric and use that to study the geometric properties. In particular, we give a formula of the S-curvature and deduce a condition for the S-curvature to be vanishing identically. Moreover, we consider the restrictive Clifford-Wolf homogeneity of left invariant (α1,α2)-metrics on compact connected simple Lie groups. We prove that, in some special cases, a restrictively Clifford-Wolf homogeneous (α1,α2)-metric must be Riemannian. An unexpected interesting observation contained in the proof reveals the fact that the S-curvature may play an important role in the study of Clifford-Wolf homogeneity in Finsler geometry.