Publication details

Geometric properties of homogeneous parabolic geometries with generalized symmetries

Authors

GREGOROVIČ Jan ZALABOVÁ Lenka

Year of publication 2016
Type Article in Periodical
Magazine / Source Differential Geometry and its Applications
MU Faculty or unit

Faculty of Science

Citation
Doi http://dx.doi.org/10.1016/j.difgeo.2016.09.008
Field General mathematics
Keywords Homogeneous parabolic geometries; Generalized symmetries; Holonomy reductions; Correspondence and twistor spaces; Invariant distributions; Invariant Weyl connections
Description 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.
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