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$(\alpha 1,\alpha 2)$-Spaces and Clifford-Wolf Homogeneity by Xu, Ming; Deng, Shaoqiang is a scholarly article available to read on EtoBox.

What is $(\alpha 1,\alpha 2)$-Spaces and Clifford-Wolf Homogeneity about?

In this paper, we introduce a new type of Finsler metrics, called $(\alpha_1,\alpha_2)$-metrics. We define the notion of the good datum of a homogeneous $(\alpha_1,\alpha_2)$-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 $(\alpha_1,\alpha_2)$-metrics on compact connected simple Lie groups. We prove that, in some special cases, a restrictively Clifford-Wolf homogeneous $(\alpha_1,\alpha_2)$-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.

Author

Xu, Ming; Deng, Shaoqiang

Published

2014

Language

EN