# Spherical harmonic d-tensors

## TL;DR

This paper develops spherical harmonic d-tensors to extend tensor harmonic techniques to Finsler geometry, enabling solutions to differential equations involving d-tensors on tangent bundles.

## Contribution

It introduces a new set of spherical harmonic d-tensors tailored for Finsler geometry, generalizing tensor harmonic methods to more complex geometric settings.

## Key findings

- Constructed a set of d-tensor harmonics for spherical symmetry
- Demonstrated application of these harmonics in Finsler geometry calculations
- Facilitated solving differential equations involving d-tensors

## Abstract

Tensor harmonics are a useful mathematical tool for finding solutions to differential equations which transform under a particular representation of the rotation group $\mathrm{SO}(3)$. The aim of this work is to make use of this tool also in the setting of Finsler geometry, or more general geometries on the tangent bundle, where the objects of relevance are d-tensors on the tangent bundle, or tensors in a pullback bundle, instead of ordinary tensors. For this purpose, we construct a set of d-tensor harmonics for spherical symmetry and show how these can be used for calculations in Finsler geometry.