  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.
