On the convex invariance in Finsler geometry

TL;DR

This paper introduces a novel approach in Finsler geometry by leveraging convex invariance of average structures, advancing the understanding of generalized Finsler geometry through geometric averaging techniques.

Contribution

It presents a new method based on convex invariance of average structures to study generalized Finsler geometry, expanding the theoretical framework.

Findings

New approach to generalized Finsler geometry

Application of geometric averaging theory

Enhanced understanding of convex invariance in Finsler structures

Abstract

As a natural application of the {\it theory of geometric averaging} in Finsler geometry and generalized Finsler geometry, a new approach to investigate {\it generalized Finsler geometry}, based on a convex invariance of the average structures, is introduced.