Symmetric parabolic contact geometries and symmetric spaces

Abstract

We discuss parabolic contact geometries carrying a smooth system of symmetries. We show that there is a symmetric space such that the parabolic geometry $$ \left( {\mathcal{G}\to M,\omega } \right) $$ is a fibre bundle over this symmetric space if and only if the base manifold M is a homogeneous reexion space. We investigate the conditions under which there is an invariant geometric structure on this symmetric space induced by the parabolic contact geometry.