Torsion-free connections on $G$-structures

Abstract

We prove that for a group ${\mathrm{SO}}_n(\mathrm{R})\subset G\subset {\mathrm{GL}}_n(\mathrm{R})$, any $G$-structure on a smooth manifold can be endowed with a torsion free connection which is locally the Levi-Civita connection of a Riemannian metric in a given conformal class. In this process, we classify the admissible groups.

arXiv comment5 pages