English

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 1|1|--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 1|1|--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.

Keywords

Cite

@article{arxiv.0901.0626,
  title  = {Symmetries of Parabolic Geometries},
  author = {Lenka Zalabova},
  journal= {arXiv preprint arXiv:0901.0626},
  year   = {2009}
}