On geometry of weakly cosymplectic manifolds
Fundamentalʹnaâ i prikladnaâ matematika, Tome 16 (2010) no. 2, pp. 33-42.

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We consider classes of weakly cosymplectic manifolds whose Riemannian curvature tensors satisfy contact analogs of the Riemannian–Christoffel identities. Additional properties of the Riemannian curvature tensor symmetry are found and a classification of weakly cosymplectic manifolds is obtained.
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V. F. Kirichenko; E. V. Kusova. On geometry of weakly cosymplectic manifolds. Fundamentalʹnaâ i prikladnaâ matematika, Tome 16 (2010) no. 2, pp. 33-42. http://geodesic.mathdoc.fr/item/FPM_2010_16_2_a3/

[1] Kirichenko V. F., “$K$-prostranstva postoyannoi golomorfnoi sektsionnoi krivizny”, Mat. zametki, 19:5 (1976), 805–814 | MR | Zbl

[2] Kirichenko V. F., “Metody obobschënnoi ermitovoi geometrii v teorii pochti kontaktnykh mnogoobrazii”, Itogi nauki i tekhn. Ser. Probl. geom. Tr. geom. sem., 18, 1986, 25–71 | MR | Zbl

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

[4] Kirichenko V. F, Arseneva O. E., Vvedenie v sovremennuyu geometriyu, TGU, Tver, 1997

[5] Kirichenko V. F., Borisovskii I. P., “Integralnye mnogoobraziya kontaktnykh raspredelenii”, Mat. sb., 189:12 (1998), 119–134 | DOI | MR | Zbl

[6] Kirichenko V. F., Lipagina L. V., “Killingovy $f$-mnogoobraziya postoyannogo tipa”, Izv. RAN. Ser. mat., 63:5 (1999), 127–146 | DOI | MR | Zbl

[7] Kirichenko V. F., Rustanov A. R., “Differentsialnaya geometriya kvazisasakievykh mnogoobrazii”, Mat. sb., 193:8 (2002), 71–100 | DOI | MR | Zbl

[8] Kobayasi Sh., Nomidzu K., Osnovy differentsialnoi geometrii, v. 1, Nauka, M., 1981

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

[10] Blair D. E., “Almost contact manifolds with Killing structure tensors”, Pacific J. Math., 39:2 (1971), 285–292 | DOI | MR | Zbl

[11] Blair D. E., Showders D. K., “Almost contact manifolds with Killing structure tensors”, J. Differential Geom., 9 (1974), 577–582 | MR | Zbl

[12] Gray A., “Nearly Kaahler manifolds”, J. Differential Geom., 4:3 (1970), 283–309 | MR | Zbl

[13] Gray A., “Curvature identities for Hermitian and almost Hermitian manifolds”, Tôhoku Math. J., 28 (1976), 601–612 | DOI | MR | Zbl

[14] Kirichenko V. F., “Sur le géométrie des variétés approximativent cosymplectiques”, C. R. Acad. Sci. Paris, 295 (1982), 673–676 | MR | Zbl

[15] Kirichenko V. F., “Generalized quasi-Kählerian manifolds and axioms of CR-submanifolds in generalized Hermitian geometry, II”, Geom. Dedicata, 52 (1994), 53–85 | DOI | MR | Zbl

[16] Proppe H., Almost contact hypersurfaces of certain almost complex manifolds, Ph. D. Thesis, McGill Univ., 1969 | MR