Geodesic
Periodic and trisymmetric spaces of interior type with simple groups of motions
Izvestiya. Mathematics , Tome 61 (1997) no. 6, pp. 1215-1229.

Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper it is shown that every periodic space of interior type with a real simple group of motions is completely determined by the set of simple roots of the reduced and irreducible root system. A relationship is established between periodic spaces with flag manifolds and Sabinin trisymmetric spaces. A certain generalization of trisymmetric spaces is considered. 
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M. P. Zamakhovskii. Periodic and trisymmetric spaces of interior type with simple groups of motions. Izvestiya. Mathematics , Tome 61 (1997) no. 6, pp. 1215-1229. http://geodesic.mathdoc.fr/item/IM2_1997_61_6_a3/

[1] Vedernikov V. I., “Ob odnom spetsialnom klasse odnorodnykh prostranstv”, Izv. vuzov. Ser. matem., 1972, no. 12, 17–22 | MR | Zbl

[2] Stepanov N. A., “Osnovnye fakty teorii $\phi $-prostranstv”, Izv. vuzov. Ser. matem., 1967, no. 3, 88–95 | MR | Zbl

[3] Stepanov N. A., “$\phi $-prostranstva v sluchae polnoi lineinoi gruppy”, Izv. vuzov. Ser. matem., 1972, no. 3, 70–79 | MR | Zbl

[4] Wolf J. A., Gray A., “Homogeneous spaces defined by Lie group automorphisms”, J. Different. Geom., 2:1–2 (1968), 77–159

[5] Fedenko A. S., Prostranstva s simmetriyami, Izd-vo BGU, Minsk, 1977 | MR | Zbl

[6] Kovalskii O., Obobschennye simmetricheskie prostranstva, Mir, M., 1984 | MR

[7] Sabinin L. V., “O geometrii subsimmetricheskikh prostranstv”, Nauchn. dokl. vyssh. shkoly. Fiz.-mat. nauki, 1958, no. 6, 127–138 | MR

[8] Sabinin L. V., “O geometrii trisimmetricheskikh rimanovykh prostranstv”, Sib. matem. zhurn., 2:2 (1961), 266–278 | MR | Zbl

[9] Sabinin L. V., “Trisimmetricheskie prostranstva s prostymi kompaktnymi gruppami dvizhenii”, Trudy semin. po vektorn. i tenzorn. analizu, no. 16, Izd-vo MGU, M., 1972, 202–226 | MR

[10] Tits J., “Sur certaines classes d'espaces homogènes de Lie”, Mèm. Acad. roy. Belg. Cl. sci., 29:3 (1955) | MR | Zbl

[11] Wolf J. A., “The action if real semisimple group in complex flag manifold, I”, Bull. Amer. Math. Soc., 75:6 (1969), 1121–1237 | DOI | MR | Zbl

[12] Rozenfeld B. A., Zamakhovskii M. P., Timoshenko T. A., “Parabolicheskie prostranstva”, Itogi nauki i tekhniki. Algebra. Topologiya. Geometriya, 26, VINITI, M., 1988, 125–160 | MR

[13] Burbaki N., Gruppy i algebry Li, gl. 4–6, Mir, M., 1972 ; гл. 7, 8, 1978 | MR | Zbl

[14] Kats V., Beskonechnomernye algebry Li, Mir, M., 1993 | MR | Zbl

[15] Komrakov B. P., “Odnorodnye prostranstva, porozhdennye avtomorfizmami, i invariantnye geometricheskie struktury”, Itogi nauki i tekhniki. Problemy geometrii, 7, VINITI, M., 1975, 81–104 | MR | Zbl

[16] Kantor I. L., “Tranzitivno-differentsialnye gruppy Li”, Trudy semin. po vektorn. i tenzorn. analizu, no. 13, Izd-vo MGU, M., 1966, 310–398 | MR

[17] Koecher M., “Imbedding of Jordan algebras”, Amer. J. of Math., 39:3 (1967), 787–816 ; 40:2 (1968), 476–510 | DOI | MR | DOI | MR

[18] Kartan E., Geometriya grupp Li i simmetricheskie prostranstva, IL, M., 1949