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Geometric properties of homogeneous parabolic geometries with generalized symmetries |
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| Affiliation: | 1. Department of Mathematics and Statistics, Faculty of Science, Masaryk University, Kotlářská 2, Brno, 611 37, Czech Republic;2. Institute of Mathematics and Biomathematics, Faculty of Science, University of South Bohemia in České Budějovice, Branišovská 1760, České Budějovice, 370 05, Czech Republic |
| 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. |
| Keywords: | Homogeneous parabolic geometries Generalized symmetries Holonomy reductions Correspondence and twistor spaces Invariant distributions Invariant Weyl connections |
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