English

General construction of symmetric parabolic structures

Differential Geometry 2012-07-30 v1

Abstract

First we introduce a generalization of symmetric spaces to parabolic geometries. We provide construction of such parabolic geometries starting with classical symmetric spaces and we show that all regular parabolic geometries with smooth systems of involutive symmetries can be obtained this way. Further, we investigate the case of parabolic contact geometries in great detail and we provide the full classification of those with semisimple groups of symmetries without complex factors. Finally, we explicitly construct all non-trivial contact geometries with non-complex simple groups of symmetries. We also indicate geometric interpretations of some of them.

Keywords

Cite

@article{arxiv.1207.0190,
  title  = {General construction of symmetric parabolic structures},
  author = {Jan Gregorovič},
  journal= {arXiv preprint arXiv:1207.0190},
  year   = {2012}
}

Comments

38 pages, to be published in Differential Geometry and Its Applications (Elsevier)