Symmetries of parabolic geometries |
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Authors: | Lenka Zalabov |
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Institution: | aMasaryk University, Brno, Czech Republic;bInternational Erwin Schrödinger Institute for Mathematical Physics, Wien, Austria |
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Abstract: | 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. |
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Keywords: | Cartan geometries Parabolic geometries |1|-graded geometries Weyl structures Symmetric spaces |
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