Integrability of canonical affinor structures of homogeneous periodic Φ-spaces
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 8 (2008), pp. 43-57.

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We study the connection between the Lie bracket on the tangent space of homogeneous periodic Φ-spaces and operators of canonical affinor structures of these spaces. The obtained relations allow us to indicate several cases of integrability of the mentioned structures.
Mots-clés : homogeneous periodic Φ-space, generalized symmetric space, affinor structure, integrability of affinor structure.
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Yu. D. Churbanov. Integrability of canonical affinor structures of homogeneous periodic $\Phi$-spaces. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 8 (2008), pp. 43-57. https://geodesic-test.mathdoc.fr/item/IVM_2008_8_a4/

[1] Stepanov N. A., “Osnovnye fakty teorii $\varphi$-prostranstv”, Izv. vuzov. Matematika, 1967, no. 3, 88–95 | MR | Zbl

[2] Kovalskii O., Obobschennye simmetricheskie prostranstva, Mir, M., 1984, 240 pp. | MR

[3] Stepanov N. A., “Odnorodnye $3$-tsiklicheskie prostranstva”, Izv. vuzov. Matematika, 1967, no. 12, 65–74 | MR | Zbl

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

[5] Gray A., “Riemannian manifolds with geodesic symmetries of order $3$”, J. Diff. Geom., 7:3–4 (1972), 343–369 | Zbl

[6] Stepanov N. A., “Pochti kompleksnye struktury na $\varphi$-prostranstvakh”, 3-ya mezhvuz. nauchn. konf. po probl. geometrii, Tezisy dokl., Kazan, 1967, 158–160 | MR

[7] Tsagas Gr., Xenos Ph., “Relation between almost complex structures and Lie bracket for a special homogeneous spaces”, Tensor, 41:3 (1984), 278–284 | MR | Zbl

[8] Xenos Ph., “Properties of the homogeneous spaces of order five”, Bull. of the Calcutta Math. Soc., 78:5 (1986), 293–302 | MR | Zbl

[9] Balaschenko V. V., Churbanov Yu. D., “Invariantnye struktury na odnorodnykh $\Phi$-prostranstvakh poryadka $5$”, UMN, 45:1 (1990), 169–170 | MR

[10] Churbanov Yu. D., “Geometriya odnorodnykh $\Phi$-prostranstv poryadka $5$”, Izv. vuzov. Matematika, 2002, no. 5, 70–81 | MR | Zbl

[11] Ermolitskii A. A., “Periodicheskie affinory i $2k$-simmetricheskie prostranstva”, DAN BSSR, 34:2 (1990), 109–111 | MR | Zbl

[12] Balaschenko V. V., Stepanov N. A., “Kanonicheskie affinornye struktury klassicheskogo tipa na regulyarnykh $\Phi$-prostranstvakh”, Matem. sb., 186:11 (1995), 3–34 | MR

[13] Churbanov Yu. D., “Geometriya spetsialnykh affinornykh struktur odnorodnykh $\Phi$-prostranstv nechetnogo poryadka”, Izv. vuzov. Matematika, 1994, no. 2, 84–86 | MR | Zbl

[14] Churbanov Yu. D., “Klassicheskie affinornye struktury odnorodnykh $\Phi$-prostranstv nechetnogo poryadka”, VII Belorussk. Matem. konf., Tez. dokl. Ch. 1, Minsk, 1996, 147–148

[15] Churbanov Yu. D., “Affinornye struktury klassicheskogo tipa odnorodnykh periodicheskikh $\Phi$-prostranstv”, VIII Belorussk. Matem. konf., Tez. dokl. Ch. 2, Minsk, 2000, 131

[16] Kobayasi Sh., Nomidzu K., Osnovy differentsialnoi geometrii, T. 1, Nauka, M., 1981, 344 pp.

[17] Dashevich O. V., “Kanonicheskie struktury klassicheskogo tipa na regulyarnykh $\Phi$-prostranstvakh i invariantnye affinnye svyaznosti”, Izv. vuzov. Matematika, 1998, no. 10, 23–31 | MR | Zbl