Explicit vector spherical harmonics on the 3-sphere

TL;DR

This paper constructs explicit one-forms on the 3-sphere that serve as a complete set of eigenmodes for the Laplace-de Rham operator, advancing the understanding of harmonic analysis on spherical manifolds.

Contribution

It introduces a new explicit family of eigenmodes for the Laplace-de Rham operator on the 3-sphere, providing tools for spectral analysis.

Findings

Complete set of eigenmodes constructed

Explicit formulas for one-forms provided

Advances spectral analysis on S^3

Abstract

We build a family of explicit one-forms on $S^3$ which are shown to form a complete set of eigenmodes for the Laplace-de Rahm operator.