# Curvature computations in Finsler Geometry using a distinguished class of anisotropic connections

## TL;DR

This paper introduces a coordinate-free method for computing tensor derivatives and curvature tensors in Finsler Geometry using anisotropic connections, paralleling classical Riemannian methods.

## Contribution

It develops a framework for tensor and curvature computations in Finsler Geometry with anisotropic connections, including Bianchi identities and comparison techniques.

## Key findings

- Derived Bianchi identities for anisotropic connection curvature tensors
- Compared curvature tensors of different anisotropic connections
- Identified a family of connections suited for Finsler metric analysis

## Abstract

We show how to compute tensor derivatives and curvature tensors using affine connections. This allows for all computations to be obtained without using coordinate systems, in a way that parallels the computations appearing in classical Riemannian Geometry. In particular, we obtain Bianchi identities for the curvature tensor of any anisotropic connection, we compare the curvature tensors of any two anisotropic connections, and we find a family of anisotropic connections which are well suited to study the geometry of Finsler metrics.