Moving frames on generalized Finsler structures

TL;DR

This paper investigates the relationship between R-Cartan structures and generalized Finsler structures on 3-manifolds, highlighting the challenges in establishing a general transformation and identifying unique mappings in special cases.

Contribution

It provides insights into the conditions under which R-Cartan and generalized Finsler structures can be related, advancing understanding of their geometric interplay.

Findings

Identifies difficulties in general transformations between structures

Determines unique mappings in specific cases

Enhances understanding of geometric relations on 3-manifolds

Abstract

We study the relation between an R-Cartan structure {\alpha} and an (I, J, K)- generalized Finsler structure on a 3-manifold showing the difficulty in finding a general transformation that maps these structures each other. In some particular cases, the mapping can be uniquely determined by geometrical conditions.