Symmetries of Parabolic Geometries
Differential Geometry
2009-09-03 v1
Abstract
We generalize the concept of affine locally symmetric spaces for parabolic geometries. We discuss mainly --graded geometries and we show some restrictions on their curvature coming from the existence of symmetries. We use the theory of Weyl structures to discuss more interesting --graded geometries which can carry a symmetry in a point with nonzero curvature. More concretely, we discuss the number of different symmetries which can exist at the point with nonzero curvature.
Cite
@article{arxiv.0901.0626,
title = {Symmetries of Parabolic Geometries},
author = {Lenka Zalabova},
journal= {arXiv preprint arXiv:0901.0626},
year = {2009}
}