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@article{877418, author = {Zalabová, Lenka}, article_location = {Amsterdam}, article_number = {5}, keywords = {Cartan geometries; Parabolic geometries; |1|-graded geometries; Weyl structures; Symmetric spaces}, language = {eng}, issn = {0926-2245}, journal = {Differential Geometry and its Applications}, title = {Symmetries of parabolic geometries}, volume = {27}, year = {2009} }
TY - JOUR ID - 877418 AU - Zalabová, Lenka PY - 2009 TI - Symmetries of parabolic geometries JF - Differential Geometry and its Applications VL - 27 IS - 5 SP - 605-622 EP - 605-622 PB - Elsevier Science SN - 09262245 KW - Cartan geometries KW - Parabolic geometries KW - |1|-graded geometries KW - Weyl structures KW - Symmetric spaces N2 - We generalize the concept of affine locally symmetric spaces for parabolic geometries. We discuss mainly |1|-graded geometries and we show some restrictions on their curvature coming from the existence of symmetries. We use the theory of Weyl structures to discuss more interesting |1|-graded geometries which can carry a symmetry in a point with nonzero curvature. More concretely, we discuss the number of different symmetries which can exist at the point with nonzero curvature. ER -
ZALABOVÁ, Lenka. Symmetries of parabolic geometries. \textit{Differential Geometry and its Applications}. Amsterdam: Elsevier Science, 2009, roč.~27, č.~5, s.~605-622. ISSN~0926-2245.
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