On strongly convex projectively flat and dually flat complex Finsler metrics

TL;DR

This paper characterizes strongly convex complex Finsler metrics that are projectively or dually flat, showing they are precisely those derived from strongly convex complex Minkowski metrics, thus linking geometric flatness to Minkowski structures.

Contribution

It establishes a complete characterization of strongly convex complex Finsler metrics that are projectively or dually flat, connecting these properties to Minkowski metrics.

Findings

Strongly convex complex Finsler metrics are projectively flat iff they derive from Minkowski metrics.

Strongly convex complex Finsler metrics are dually flat iff they derive from Minkowski metrics.

The characterization provides a geometric criterion for flatness in complex Finsler geometry.

Abstract

In this paper, we prove that a strongly convex complex Finsler metric $F$ on a domain $D\subset\mathbb{C}^n$ is projectively flat (resp. dually flat) if and only if $F$ comes from a strongly convex complex Minkowski metric.