Invariant Finsler metrics on homogeneous manifolds: II. Complex structures

Abstract

In this paper, we study homogeneous complex Finsler spaces. We first prove that each homogeneous complex Finsler space can be written as a coset space of a Lie group with an invariant complex structure as well as an invariant complex Finsler metric. We then introduce the notion of Minkowski representations of Lie groups and Lie algebras to give a complete algebraic description for such spaces. Finally, we study symmetric complex Finsler spaces and obtain a complete classification of such spaces.