On two theorems about local automorphisms of geometric structures
Differential Geometry
2020-05-20 v1
Abstract
This article investigates a few questions about orbits of local automorphisms in manifolds endowed with rigid geometric structures. We give sufficient conditions for local homogeneity in a broad class of such structures, namely Cartan geometries, extending a classical result of Singer about locally homogeneous Riemannian manifolds. We also revisit a strong result of Gromov which describes the structure of the orbits of local automorphisms of manifolds endowed with -rigid structures, and give a statement of this result in the setting of Cartan geometries.
Cite
@article{arxiv.1402.5048,
title = {On two theorems about local automorphisms of geometric structures},
author = {Vincent Pecastaing},
journal= {arXiv preprint arXiv:1402.5048},
year = {2020}
}