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Geometric properties of homogeneous parabolic geometries with generalized symmetries. (English) Zbl 1352.53020
Summary: We investigate geometric properties of homogeneous parabolic geometries with generalized symmetries. We show that they can be reduced to 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.

##### MSC:
 53C10 $$G$$-structures 53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.) 53C29 Issues of holonomy in differential geometry 53C30 Differential geometry of homogeneous manifolds 58D19 Group actions and symmetry properties 58J70 Invariance and symmetry properties for PDEs on manifolds
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