Publication details
Symmetries of parabolic geometries
| Authors | |
|---|---|
| Year of publication | 2009 |
| Type | Article in Periodical |
| Magazine / Source | Differential Geometry and its Applications |
| MU Faculty or unit | |
| Citation | |
| 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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