Article
Keywords:
local reflexion space; flat Cartan geometry; local infinitesimal automorphisms
Summary:
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.
References:
                        
[2] Čap, A., Slovák, J.: 
Parabolic Geometries I: Background and General Theory. Math. Surveys Monogr. 154 (2009). 
MR 2532439 | 
Zbl 1183.53002 
[3] Kolář, I., Michor, P. W., Slovák, J.: 
Natural Operations in Differential Geometry. Springer Verlag, Berlin–Heidelberg, 1993. 
MR 1202431 
[5] Loos, O.: 
An intrinsic characterization of fibre bundles associated with homogeneous spaces defined by Lie group automorphisms. Abh. Math. Sem. Univ. Hamburg 37 (1972), 160–179. 
DOI 10.1007/BF02999694 | 
MR 0307124 | 
Zbl 0239.55018 
[6] Sharpe, R. W.: 
Differential Geometry, Cartan’s Generalization of Klein’s Erlangen Program. Springer Verlag, New York, 1997. 
MR 1453120 | 
Zbl 0876.53001