# K\"ahler Finsler Metrics and Conformal Deformations

## TL;DR

This paper explores the conformal properties of complex Finsler metrics, characterizing when they are globally conformal K"ahler, analyzing curvature functionals, and addressing a Yamabe-type problem in this setting.

## Contribution

It provides a characterization of conformal K"ahler structures on complex Finsler manifolds and studies the stability and critical points of curvature functionals.

## Key findings

- Characterization of globally conformal K"ahler complex Finsler manifolds
- Analysis of critical points of total holomorphic and Ricci curvature
- Results on stability of K"ahler Finsler metrics and a Yamabe type problem

## Abstract

The conformal properties of complex Finsler metrics are studied. We give a characterization of a compact complex Finsler manifold to be globally conformal K\"ahler. The critical points of the total holomorphic curvature and total Ricci curvature in the volume preserved conformal classes are studied. The stability of critical K\"ahler Finsler metrics is obtained. A Yamabe type problem for mean Ricci curvature is considered.