Publication details

General construction of symmetric parabolic structures

Investor logo


Year of publication 2012
Type Article in Periodical
Magazine / Source Differential Geometry and its Applications
MU Faculty or unit

Faculty of Science

Field General mathematics
Keywords Parabolic geometries; Contact geometries; Symmetric spaces; Extension functors
Description 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 in 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.
Related projects:

You are running an old browser version. We recommend updating your browser to its latest version.

More info