On Finslerized Absolute Parallelism spaces

TL;DR

This paper constructs a new geometric space called Finslerized Parallelizable space by integrating Finsler and Absolute Parallelism geometries, aiming to enhance applications in physical theories.

Contribution

It introduces a novel Finsler structure within GAP-spaces, combining features of both geometries for potential use in physical modeling.

Findings

Derived five connections and their torsion and curvature tensors.

Identified special Finslerized Parallelizable spaces.

Explored the interrelation between Finsler and GAP geometries.

Abstract

The aim of the present paper is to construct and investigate a Finsler structure within the framework of a Generalized Absolute Parallelism space (GAP-space). The Finsler structure is obtained from the vector fields forming the parallelization of the GAP-space. The resulting space, which we refer to as a Finslerized Parallelizable space, combines within its geometric structure the simplicity of GAP-geometry and the richness of Finsler geometry, hence is potentially more suitable for applications and especially for describing physical phenomena. A study of the geometry of the two structures and their interrelation is carried out. Five connections are introduced and their torsion and curvature tensors derived. Some special Finslerized Parallelizable spaces are singled out. One of the main reasons to introduce this new space is that both Absolute Parallelism and Finsler geometries have proved effective in the formulation of physical theories, so it is worthy to try to build a more general geometric structure that would share the benefits of both geometries.