Torsion-free connections on $G$-structures

Brice Flamencourt

doi:10.1016/j.difgeo.2023.102075

Torsion-free connections on $G$-structures

Differential Geometry 2024-06-24 v2

Authors: 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.

Keywords

lie groups algebraic varieties holonomy

Cite

@article{arxiv.2212.11025,
  title  = {Torsion-free connections on $G$-structures},
  author = {Brice Flamencourt},
  journal= {arXiv preprint arXiv:2212.11025},
  year   = {2024}
}

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5 pages

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