Diffeomorphisms and orthonormal frames

TL;DR

This paper investigates the uniqueness of a natural homomorphism from local vector fields to local rotations on Riemannian manifolds, establishing its uniqueness near flat metrics.

Contribution

It proves the homomorphism's uniqueness in the perturbative regime around the flat metric, clarifying its mathematical structure.

Findings

Homomorphism is unique near flat metrics.

Addresses the mathematical structure of local vector fields and rotations.

Provides a positive answer to the uniqueness question in a specific regime.

Abstract

There is a natural homomorphism of Lie pseudoalgebras from local vector fields to local rotations on a Riemannian manifold. We address the question whether this homomorphism is unique and give a positive answer in the perturbative regime around the flat metric.