Local Generalized Symmetries and Locally Symmetric Parabolic Geometries
Differential Geometry
2017-05-24 v4
Abstract
We investigate (local) automorphisms of parabolic geometries that generalize geodesic symmetries. We show that many types of parabolic geometries admit at most one generalized geodesic symmetry at a point with non-zero harmonic curvature. Moreover, we show that if there is exactly one symmetry at each point, then the parabolic geometry is a generalization of an affine (locally) symmetric space.
Keywords
Cite
@article{arxiv.1607.01965,
title = {Local Generalized Symmetries and Locally Symmetric Parabolic Geometries},
author = {Jan Gregorovič and Lenka Zalabová},
journal= {arXiv preprint arXiv:1607.01965},
year = {2017}
}