Some elementary observations regarding reductive Cartan geometries
Differential Geometry
2023-07-06 v4
Abstract
After defining generalizations of the notions of covariant derivatives and geodesics from Riemannian geometry for reductive Cartan geometries in general, various results for reductive Cartan geometries analogous to important elementary results from Riemannian geometry are proven using these generalizations. In particular, a generalization of the Hopf-Rinow theorem is given with a pleasantly concise proof.
Cite
@article{arxiv.1607.01451,
title = {Some elementary observations regarding reductive Cartan geometries},
author = {Jacob W. Erickson},
journal= {arXiv preprint arXiv:1607.01451},
year = {2023}
}
Comments
I wrote this during my first year as an undergrad, and it does not meet my current quality standards. Also, one central claim appears to be wrong: geodesic completeness might not actually imply completeness