Geometric properties of homogeneous parabolic geometries with generalized symmetries

Abstract

We investigate geometric properties of homogeneous parabolic geometries with generalized symmetries. We show that they can be reduced to a simpler geometric structures and interpret them explicitly. For specific types of parabolic geometries, we prove that the reductions correspond to known generalizations of symmetric spaces. In addition, we illustrate our results on an explicit example and provide a complete classification of possible non--trivial cases.

arXiv comment37 pp, In order to better emphasize our main results, we reorganized our manuscript and improved the presentation of the results