Holomorphic curvature of Finsler metrics and complex geodesics

Holomorphic Curvature of Finsler Metrics and Complex Geodesics

If D is a bounded convex domain in C , then the work of Lempert [L] and Royden-Wong [RW] (see also [A]) show that given any point p ∈ D and any non-zero tangent vector v ∈ C at p, there exists a holomorphic map φ:U → D from the unit disk U ⊂ C into D passing through p and tangent to v in p which is an isometry with respect to the hyperbolic distance of U and the Kobayashi distance of D. Further...

The Holomorphic Bisectional Curvature of the Complex Finsler Spaces

The notion of holomorphic bisectional curvature for a complex Finsler space (M, F ) is defined with respect to the Chern complex linear connection on the pull-back tangent bundle. By means of holomorphic curvature and holomorphic flag curvature of a complex Finsler space, a special approach is emloyed to obtain the characterizations of the holomorphic bisectional curvature. For the class of gen...

Homogeneous geodesics of left invariant Finsler metrics

In this paper, we study the set of homogeneous geodesics of a leftinvariant Finsler metric on Lie groups. We first give a simple criterion that characterizes geodesic vectors. As an application, we study some geometric properties of bi-invariant Finsler metrics on Lie groups. In particular a necessary and sufficient condition that left-invariant Randers metrics are of Berwald type is given. Fin...

Nonreversible Finsler Metrics of Positive Flag Curvature

Projectively Flat Finsler Metrics of Constant Curvature

It is the Hilbert’s Fourth Problem to characterize the (not-necessarilyreversible) distance functions on a bounded convex domain in R such that straight lines are shortest paths. Distance functions induced by a Finsler metric are regarded as smooth ones. Finsler metrics with straight geodesics said to be projective. It is known that the flag curvature of any projective Finsler metric is a scala...