Geodesic
Local reflexion spaces
Archivum mathematicum, Tome 48 (2012) no. 5, pp. 323-332 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
DOI : 10.5817/AM2012-5-323
Classification : 53C10, 53C35
Keywords: local reflexion space; flat Cartan geometry; local infinitesimal automorphisms 
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Gregorovič, Jan. Local reflexion spaces. Archivum mathematicum, Tome 48 (2012) no. 5, pp. 323-332. doi: 10.5817/AM2012-5-323

[1] Alekseevsky, D. V., Michor, P. W.: Differential geometry of $\mathfrak{g}$–manifolds. Differential Geom. Appl. 5 (1995), 371–403. | DOI | MR

[2] Čap, A., Slovák, J.: Parabolic Geometries I: Background and General Theory. Math. Surveys Monogr. 154 (2009). | MR | Zbl

[3] Kolář, I., Michor, P. W., Slovák, J.: Natural Operations in Differential Geometry. Springer Verlag, Berlin–Heidelberg, 1993. | MR

[4] Loos, O.: Spiegelungsräume und homogene symmetrische Räume. Math. Z. 99 (1967), 141–170. | DOI | MR | Zbl

[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 | MR | Zbl

[6] Sharpe, R. W.: Differential Geometry, Cartan’s Generalization of Klein’s Erlangen Program. Springer Verlag, New York, 1997. | MR | Zbl

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