Geometric structures invariant to symmetries
The aim of this book is to generalize symmetric spaces to several geometric strctures. The first and third chapter of this work contain description of several geometric structures, for which we want to define the symmetries. This is done in the second chapter and at the end end of the third chapter. The second chapter also explains, how the classical symmetric spaces fit in our approach, and investigates geometric structures on symmetric spaces. In the fourth and fifth chapters, we investigate and construct examples of symmetric parabolic geometries in the simplest cases. In fact, we obtain classification of non-flat symmetric AHS-structures and parabolic contact structures in the case when the groups generated by the symmetries are semisimple, and we explicitly construct many of them. For the convenience of the reader, the appendices display tables containing the classification of simple symmetric spaces and tables containing the gradings associated to the parabolic geometries, which we are investigating.
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