SYMMETRIC PARABOLIC CONTACT GEOMETRIES AND SYMMETRIC SPACES

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Authors	GREGOROVIČ Jan ZALABOVÁ Lenka
Year of publication	2013
Type	Article in Periodical
Magazine / Source	Transformation Groups
MU Faculty or unit	Faculty of Science
Citation
Doi	https://doi.org/10.1007/s00031-013-9231-z
Field	General mathematics
Keywords	parabolic contact geometry; symmetric spaces; homogeneous spaces; invariant geometric structures
Description	We discuss parabolic contact geometries carrying a smooth system of symmetries. We show that there is a symmetric space such that the parabolic geometry (G -> M, w) is a fibre bundle over this symmetric space if and only if the base manifold M is a homogeneous reflexion space. We investigate the conditions under which there is an invariant geometric structure on this symmetric space induced by the parabolic contact geometry.
Related projects:	Algebraic and geometric methods and structures