Publication details

Symmetries of almost Grassmannian geometries



Year of publication 2008
Type Article in Proceedings
Conference Differential geometry and its applications
MU Faculty or unit

Faculty of Science

Field General mathematics
Keywords Cartan geometries; parabolic geometries; almost Grassmannian structures; almost quaternionic structures; symmetric spaces
Description We study symmetries of almost Grassmannian and almost quaternionic structures. We generalize the classical definition for locally symmetric spaces and we discuss the existence of symmetries on the homogeneous models. We proves the local flatness of the symmetric geometries for most cases of almost Grassmannian geometries. There are also some more interesting types of almost Grassmannian and almost quaternionic geometries, which can carry some symmetry in the point with nonzero curvature. We show, that there can be at most one symmetry in such point.
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