Geodesic
Weakly symmetric Riemannian manifolds with reductive isometry group
Sbornik. Mathematics, Tome 195 (2004) no. 4, pp. 599-614 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

A classification of non-symmetric weakly symmetric Riemannian manifolds with reductive symmetry group is obtained. In particular, all compact weakly symmetric Riemannian manifolds are described. Many new examples of weakly symmetric manifolds are constructed. 
@article{SM_2004_195_4_a5,
     author = {O. S. Yakimova},
     title = {Weakly symmetric {Riemannian} manifolds with reductive isometry group},
     journal = {Sbornik. Mathematics},
     pages = {599--614},
     year = {2004},
     volume = {195},
     number = {4},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2004_195_4_a5/}
}
TY  - JOUR
AU  - O. S. Yakimova
TI  - Weakly symmetric Riemannian manifolds with reductive isometry group
JO  - Sbornik. Mathematics
PY  - 2004
SP  - 599
EP  - 614
VL  - 195
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/SM_2004_195_4_a5/
LA  - en
ID  - SM_2004_195_4_a5
ER  - 
%0 Journal Article
%A O. S. Yakimova
%T Weakly symmetric Riemannian manifolds with reductive isometry group
%J Sbornik. Mathematics
%D 2004
%P 599-614
%V 195
%N 4
%U http://geodesic.mathdoc.fr/item/SM_2004_195_4_a5/
%G en
%F SM_2004_195_4_a5
O. S. Yakimova. Weakly symmetric Riemannian manifolds with reductive isometry group. Sbornik. Mathematics, Tome 195 (2004) no. 4, pp. 599-614. http://geodesic.mathdoc.fr/item/SM_2004_195_4_a5/

[1] Cartan É., “Sur une classe remarquable d'espaces de Riemann. I, II”, Bull. Soc. Math. France, 54 (1926), 214–264 ; 55 (1927), 114–134 | MR | MR

[2] Helgason S., Differential geometry, Lie groups, and symmetric spaces, Pure Appl. Math., 80, Academic Press, New York, 1978 | MR | Zbl

[3] Berndt J., Prüfer F., Vanhecke L., “Symmetric-like Riemannian manifolds and geodesic symmetries”, Proc. Roy. Soc. Edinburgh, Sect. A, 125 (1995), 265–282 | MR | Zbl

[4] Selberg A., “Harmonic analysis and discontinuous groups in weakly symmetric Riemannian spaces with applications to Dirichlet series”, J. Indian Math. Soc. (N.S.), 20 (1956), 47–87 | MR | Zbl

[5] Berndt J., Kowalski O., Vanhecke L., “Geodesics in weakly symmetric spaces”, Ann. Global Anal. Geom., 15 (1997), 153–156 | DOI | MR | Zbl

[6] Berndt J., Vanhecke L., “Geometry of weakly symmetric spaces”, J. Math. Soc. Japan, 48 (1996), 745–760 | DOI | MR | Zbl

[7] Nagai S., “Weakly symmetric spaces in complex and quaternionic space forms”, Arch. Math. (Basel), 65 (1995), 342–351 | MR | Zbl

[8] Akhiezer D. N., Vinberg E. B., “Weakly symmetric spaces and spherical varieties”, Transform. Groups, 4 (1999), 12–46 | DOI | MR

[9] Vinberg E. B., “Kommutativnye odnorodnye prostranstva i koizotropnye deistviya”, UMN, 56:1 (2001), 3–62 | MR | Zbl

[10] Yakimova O. S., “Pravilnye izometrii slabo simmetricheskikh odnorodnykh prostranstv”, Matem. sb., 193:1 (2002), 143–156 | MR | Zbl

[11] Onischik A. L., “Otnosheniya vklyucheniya mezhdu tranzitivnymi kompaktnymi gruppami preobrazovanii”, Trudy MMO, 11, 1962, 199–242 | MR | Zbl

[12] Fels G., “A note on homogeneous locally symmetric spaces”, Transform. Groups, 2 (1997), 269–277 | DOI | MR | Zbl

[13] Yakimova O. S., “Slabo simmetricheskie prostranstva poluprostykh grupp Li”, Vestn. MGU. Ser. 1. Matem., mekh., 2002, no. 2, 57–60 | MR | Zbl

[14] Brion M., “Classification des espaces homogènes sphériques”, Compositio Math., 63 (1987), 189–208 | MR | Zbl

[15] Mikityuk I. V., “Ob integriruemosti invariantnykh gamiltonovykh sistem s odnorodnymi konfiguratsionnymi prostranstvami”, Matem. sb., 129 (1986), 514–546 | MR | Zbl

[16] Krämer M., “Sphärische Untergruppen in kompakten zusammenhängenden Liegruppen”, Compositio Math., 38 (1979), 129–153 | MR | Zbl

[17] Karpelevich F. I., “Poverkhnosti tranzitivnosti poluprostoi podgruppy gruppy dvizhenii simmetricheskogo prostranstva”, Dokl. AN SSSR, 93:3 (1953), 401–404 | Zbl