Local Generalized Symmetries and Locally Symmetric Parabolic Geometries

[摘要] We investigate (local) automorphisms of parabolic geometries that generalize geodesic symmetries. We show that many types of parabolic geometries admit at most one generalized geodesic symmetry at a point with non-zero harmonic curvature. Moreover, we show that if there is exactly one symmetry at each point, then the parabolic geometry is a generalization of an affine (locally) symmetric space.

[关键词] parabolic geometries;generalized symmetries;generalizations of symmetric spaces;automorphisms with fixe