Local generalized symmetries and locally symmetric parabolic geometries

Jan Gregorovič, Lenka Zalabová

Published 2016-07-07Version 1

We investigate distinguished classes of (local) automorphisms of parabolic geometries that are related to natural geodesics transformations of Weyl connections. These transformations generalize the geodesic symmetries and we call them generalized symmetries. We classify for which parabolic geometries, there is at most one generalized symmetry from given class at some point. For these geometries we classify, when all generalized symmetries are natural geodesics transformations of the same Weyl connection, which particularly means that the parabolic geometry is a generalization of (locally) symmetric space.