Local reflexion spaces

Jan Gregorovič

Address: Department of Mathematics and Statistics, Faculty of Sciences, Masaryk University, Kotlářská 2, Brno, 611 37, Czech Republic

E-mail: jan.gregorovic@seznam.cz

Abstract: A reflexion space is generalization of a symmetric space introduced by O. Loos in [4]. We generalize locally symmetric spaces to local reflexion spaces in the similar way. We investigate, when local reflexion spaces are equivalently given by a locally flat Cartan connection of certain type.

AMSclassification: primary 53C35; secondary 53C10.

Keywords: local reflexion space, flat Cartan geometry, local infinitesimal automorphisms.

DOI: 10.5817/AM2012-5-323