Finsleroid--Finsler Parallelism

TL;DR

This paper explores the invariance of the Finsleroid-induced scalar product and angle under parallel transport in Landsberg spaces, introducing a two-vector extension of the Finsleroid metric tensor.

Contribution

It introduces a two-vector extension of the Finsleroid metric tensor and demonstrates the invariance of the scalar product and angle under parallel transport in Landsberg spaces.

Findings

Scalar product and angle remain unchanged under Finsleroid-type parallel transport in Landsberg spaces.

Proposes a two-vector extension of the Finsleroid metric tensor.

Establishes invariance properties in the Finsleroid framework.

Abstract

The Finsleroid--induced scalar product, and hence the angle, proves to remain unchanged under the Finsleroid--type parallel transportation of involved vectors in the Landsberg case. The two--vector extension of the Finsleroid metric tensor is proposed.