Publication details

Symmetries of parabolic geometries

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Year of publication 2009
Type Article in Periodical
Magazine / Source Differential Geometry and its Applications
MU Faculty or unit

Faculty of Science

Field General mathematics
Keywords Cartan geometries; Parabolic geometries; |1|-graded geometries; Weyl structures; Symmetric spaces
Description 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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