Normal homogeneous Finsler spaces

Ming Xu; Shaoqiang Deng

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arXiv · 1411.3053

Normal homogeneous Finsler spaces

Ming Xu·Shaoqiang Deng

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Abstract

In this paper, we study normal homogeneous Finsler spaces. We first define the notion of a normal homogeneous Finsler space, using the method of isometric submersion of Finsler metrics. Then we study the geometric properties. In particular, we establish a technique to reduce the classification of normal homogeneous Finsler spaces of positive flag curvature to an algebraic problem. The main result of this paper is a classification of positively curved normal homogeneous Finsler spaces. It turns out that a coset space $G/H$ admits a positively curved normal homogeneous Finsler metric if and only if it admits a positively curved normal homogeneous Riemannian metric. We will also give a complete description of the coset spaces admitting non-Riemannian positively curved normal homogeneous Finsler spaces.

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BibTeX RIS

Ming Xu, Shaoqiang Deng. 2014-11-12. Normal homogeneous Finsler spaces. https://arxiv.org/abs/1411.3053

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