负曲率齐性Finsler流形的Heintze-Kobayashi-Wolf理论
Heintze-Kobayashi-Wolf theory for negatively curved homogeneous Finsler manifolds
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中文总结 AI 辅助
该研究将Heintze-Kobayashi-Wolf理论推广至齐性Finsler几何，证明连通负曲率齐性Finsler流形等距于单连通可解李群的左不变度量空间，且Heintze判别准则是实可解李代数生成对应李群的充要条件。
中文摘要 AI 辅助
本文通过证明两个主要定理，将Heintze-Kobayashi-Wolf理论推广到齐性Finsler几何领域。第一，任何连通的负曲率齐性Finsler流形都等距于一个配备左不变度量的李群，且该李群必为单连通可解李群。第二，Heintze判别准则中的条件，对实可解李代数生成容许负曲率左不变Finsler度量的李群而言是充要的。
英文摘要
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.
