Projectively related complex Finsler metrics

TL;DR

This paper explores projectively related complex Finsler metrics, establishing key theorems, characterizations, and applications, including a complex version of Hilbert's Fourth Problem and analysis of complex Randers metrics.

Contribution

It introduces the complex versions of classical theorems, characterizes special classes of complex Finsler metrics, and applies these results to specific metric types.

Findings

Proved complex versions of Rapcsák's theorem.

Characterized weakly Kähler and generalized Berwald projectively related metrics.

Described the projectiveness of complex Randers metrics.

Abstract

In this paper we introduce in study the projectively related complex Finsler metrics. We prove the complex versions of the Rapcs\'{a}k's theorem and characterize the weakly K\"{a}hler and generalized Berwald projectively related complex Finsler metrics. The complex version of Hilbert's Fourth Problem is also pointed out. As an application, the projectiveness of a complex Randers metric is described.