Recent progress on homogeneous Finsler spaces with positive curvature

TL;DR

This survey reviews recent advances in classifying positively curved homogeneous Finsler spaces, highlighting key results, methods, and open problems in the field of differential geometry.

Contribution

It consolidates recent research findings on homogeneous Finsler spaces with positive curvature and discusses unresolved questions for future exploration.

Findings

Classification of positively curved homogeneous Finsler spaces

Identification of key open problems in the field

Summary of recent methods and results

Abstract

This is a survey paper on our recent works concerning the classification of positively curved homogeneous Finsler spaces, and some related topics. At the final part, we present some open problems in this field.