Characterizations of complex Finsler connections and weakly complex Berwald metrics

Projective complex Finsler metrics

In this paper we obtain the conditions in which two complex Finsler metrics are projective, i.e. have the same geodesics as point sets. Two important classes of such metrics are submitted to our attention: conformal projective and weakly projective complex Finsler spaces. For each of them we study the transformations of the canonical connection. We pay attention for local projectivity with a pu...

Beil metrics in complex Finsler geometry

In this paper we continue the study of the complex Beil metrics, in complex Finsler geometry, [18]. Primarily, we determine the main geometric objects corresponding to these metrics, e.g. the Chern-Finsler complex non-linear connection, the Chern-Finsler complex linear connection and the holomorphic curvature. We focus our study on the cases when a complex Finsler space, endowed with a complex ...

Two-dimensional Complex Berwald Spaces with (α, Β)-metrics

In this paper we study the two-dimensional complex Finsler spaces with (α, β)-metrics by using the complex Berwald frame. A special approach is dedicated to the complex Berwald spaces with (α, β) metrics. We establish the necessary and sufficient condition so that the complex Randers and Kropina spaces should be complex Berwald spaces, and we will illustrate the existence of these spaces in som...

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...

Properties of Generalized Berwald Connections