Nearly K\"ahler and Hermitian $f$-structures on homogeneous $\Phi$-spaces of order~6
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 4 (2011), pp. 89-98.

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In this paper we consider the canonical $f$-structures on arbitrary naturally reductive homogeneous $\Phi$-spaces of order 6. We obtain the necessary and sufficient conditions under which these structures belong to classes of a generalized Hermitian geometry such as nearly Kähler and Hermitian $f$-structures.
Keywords: naturally reductive space, generalized Hermitian geometry, homogeneous periodic $\Phi$-space, generalized symmetric space, canonical $f$-structure.
Mots-clés : invariant $f$-structure
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     title = {Nearly {K\"ahler} and {Hermitian} $f$-structures on homogeneous $\Phi$-spaces of order~6},
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A. S. Samsonov. Nearly K\"ahler and Hermitian $f$-structures on homogeneous $\Phi$-spaces of order~6. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 4 (2011), pp. 89-98. http://geodesic.mathdoc.fr/item/IVM_2011_4_a8/

[1] Yano K., “On a structure defined by a tensor field $f$ of type $(1,1)$ satisfying $f^3+f=0$”, Tensor, 14 (1963), 99–109 | MR | Zbl

[2] Yano K., Kon M., $CR$-podmnogoobraziya v kelerovom i sasakievom mnogoobraziyakh, Nauka, M., 1990 | MR

[3] Kirichenko V. F., “Metody obobschennoi ermitovoi geometrii v teorii pochti kontaktnykh mnogoobrazii”, Itogi nauki i tekhn. Prob. geom., 18, VINITI AN SSSR, 1986, 25–71 | MR | Zbl

[4] Kirichenko V. F., “Kvaziodnorodnye mnogoobraziya i obobschennye pochti ermitovy struktury”, Izv. AN SSSR. Ser. matem., 47:6 (1983), 1208–1223 | MR | Zbl

[5] Kirichenko V. F., Differentsialno-geometricheskie struktury na mnogoobraziyakh, MPGU, M., 2003

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

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

[8] Fedenko A. S., Prostranstva s simmetriyami, Izd-vo Belorusskogo un-ta, Minsk, 1977 | MR | Zbl

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

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

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

[12] Balaschenko V. V., “Kanonicheskie $f$-struktury giperbolicheskogo tipa na regulyarnykh $\Phi$-prostranstvakh”, UMN, 53:4 (1998), 213–214 | MR | Zbl

[13] Balaschenko V. V., “Estestvenno reduktivnye killingovy $f$-mnogoobraziya”, UMN, 54:3 (1999), 151–152 | MR | Zbl

[14] Balaschenko V. V., “Odnorodnye ermitovy $f$-mnogoobraziya”, UMN, 56:3 (2001), 159–160 | MR | Zbl

[15] Balaschenko V. V., “Odnorodnye priblizhenno kelerovy $f$-mnogoobraziya”, Dokl. RAN, 376:4 (2001), 439–441 | MR

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

[17] Balaschenko V. V., Vylegzhanin D. V., “Obobschennaya ermitova geometriya na odnorodnykh $\Phi$-prostranstvakh konechnogo poryadka”, Izv. vuzov. Matematika, 2004, no. 10, 33–44 | MR | Zbl

[18] Balashchenko V. V., “Invariant structures generated by Lie group automorphisms on homogeneous spaces”, Proc. of the Workshop “Contemporary Geometry and Related Topics” (Belgrade, Yugoslavia, May 15–21, 2002), eds. N. Bokan, M. Djoric, A. T. Fomenko, Z. Rakic, J. Wess, World Scientific, 2004, 1–32 | DOI | MR | Zbl

[19] Balaschenko V. V., Nikonorov Yu. G., Rodionov E. D., Slavskii V. V., Odnorodnye prostranstva: teoriya i prilozheniya, Poligrafist, Khanty-Mansiisk, 2008

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

[21] Kirichenko V. F., “O geometrii odnorodnykh $K$-prostranstv”, Matem. zametki, 30:4 (1981), 569–582 | MR | Zbl

[22] Balashchenko V. V., “Invariant nearly Kähler $f$-structures on homogeneous spaces”, Global Differential Geometry: The mathematical legacy of Alfred Gray, Contemporary Mathematics, 288, 2001, 263–267 | MR | Zbl

[23] Kobayasi Sh., Nomidzu K., Osnovy differentsialnoi geometrii, v. 2, Nauka, M., 1981

[24] Balaschenko V. V., “Invariantnye $f$-struktury na estestvenno reduktivnykh odnorodnykh prostranstvakh”, Izv. vuzov. Matematika, 2008, no. 4, 3–15 | MR | Zbl

[25] Churbanov Yu. D., “Integriruemost kanonicheskikh affinornykh struktur odnorodnykh periodicheskikh $\Phi$-prostranstv”, Izv. vuzov. Matematika, 2008, no. 8, 43–57 | MR | Zbl

[26] Samsonov A. S., “Odnorodnye $\Phi$-prostranstva psevdoortogonalnykh grupp $O(2,k)$”, Vestn. BGU. Ser. 1. Matem. Fiz. Inform., 2007, no. 3, 112–118 | MR | Zbl