Torsion-free connections on $G$-structures

Brice Flamencourt

doi:10.1016/j.difgeo.2023.102075

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arXiv · 2212.11025

Torsion-free connections on $G$-structures

Brice Flamencourt

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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.

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BibTeX RIS

Brice Flamencourt. 2022-12-21. Torsion-free connections on $G$-structures. https://doi.org/10.1016/j.difgeo.2023.102075

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