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arXiv · 2306.08524

Heintze-Kobayashi-Wolf theory for negatively curved homogeneous Finsler manifolds

Ming Xu
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Abstract

In this paper, we generalize the Heintze-Kobayashi-Wolf theory to homogeneous Finsler geometry, by proving two main theorems. First, any connected negatively curved homogeneous Finsler manifold is isometric to a Lie group endowed with a left invariant metric, and that Lie group must be simply connected and solvable. Second, the requirement in Heintze's criterion is necessary and sufficient for a real solvable Lie algebra to generate a Lie group which admits negatively curved left invariant Finsler metrics.

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Ming Xu. 2023-06-14. Heintze-Kobayashi-Wolf theory for negatively curved homogeneous Finsler manifolds. https://arxiv.org/abs/2306.08524

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