Symmetric parabolic contact geometries and symmetric spaces |
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| Authors: | Jan Gregorovi? Lenka Zalabová |
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| Institution: | 1. Department of Mathematics and Statistics, Faculty of Sciences, Masaryk University, Kotlá?ská 2, Brno, 611 37, Czech Republic
2. Institute of Mathematics and Biomathematics, Faculty of Science, University of South Bohemia, Brani?ovská 31, ?eské Budějovice, 370 05, Czech Republic
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| 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. |
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