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

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.