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