Geodesic
Almost $C(\lambda)$-manifolds
Fundamentalʹnaâ i prikladnaâ matematika, Tome 16 (2010) no. 2, pp. 139-146.

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

In this paper, we study almost $C(\lambda)$-manifolds. We obtain necessary and sufficient conditions for an almost contact metric manifold to be an almost $C(\lambda)$-manifold. We prove that contact analogs of A. Gray's second and third curvature identities on almost $C(\lambda)$-manifolds hold, while a contact analog of A. Gray's first identity holds if and only if the manifold is cosymplectic. It is proved that a conformally flat, almost $C(\lambda)$-manifold is a manifold of constant curvature $\lambda$. 
@article{FPM_2010_16_2_a13,
     author = {S. V. Kharitonova},
     title = {Almost $C(\lambda)$-manifolds},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {139--146},
     publisher = {mathdoc},
     volume = {16},
     number = {2},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2010_16_2_a13/}
}
TY  - JOUR
AU  - S. V. Kharitonova
TI  - Almost $C(\lambda)$-manifolds
JO  - Fundamentalʹnaâ i prikladnaâ matematika
PY  - 2010
SP  - 139
EP  - 146
VL  - 16
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/FPM_2010_16_2_a13/
LA  - ru
ID  - FPM_2010_16_2_a13
ER  - 
%0 Journal Article
%A S. V. Kharitonova
%T Almost $C(\lambda)$-manifolds
%J Fundamentalʹnaâ i prikladnaâ matematika
%D 2010
%P 139-146
%V 16
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/FPM_2010_16_2_a13/
%G ru
%F FPM_2010_16_2_a13
S. V. Kharitonova. Almost $C(\lambda)$-manifolds. Fundamentalʹnaâ i prikladnaâ matematika, Tome 16 (2010) no. 2, pp. 139-146. http://geodesic.mathdoc.fr/item/FPM_2010_16_2_a13/

[1] Besse A., Mnogoobraziya Einshteina, Mir, M., 1990 | MR | Zbl

[2] Volkova E. S., “Tozhdestva krivizny normalnykh mnogoobrazii killingova tipa”, Mat. zametki, 62:3 (1997), 351–362 | DOI | MR | Zbl

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

[4] Kirichenko V. F., “Obobschënnye klassy Greya–Khervelly i golomorfno-proektivnye preobrazovaniya obobschënnykh pochti ermitovykh struktur”, Izv. RAN. Ser. mat., 69:5 (2005), 107–132 | DOI | MR | Zbl

[5] Kirichenko V. F., Tretyakova I. V., “O postoyanstve tipa pochti ermitovykh mnogoobrazii”, Mat. zametki, 68:5 (2000), 668–676 | DOI | MR | Zbl

[6] Rashevskii P. K., Rimanova geometriya i tenzornyi analiz, Nauka, M., 1964 | MR | Zbl

[7] Gray A., “Curvature identities for Hermitian and almost Hermitian manifolds”, Tôhoku Math. J., 28:4 (1976), 601–812 | DOI | MR

[8] Janssen D., Vanhecke L., “Almost contact structures and curvature tensors”, Kodai Math. J., 4 (1981), 1–27 | DOI | MR | Zbl

[9] Olszak Z., “Locally conformal almost cosymplectic manifolds”, Colloq. Math., 57:1 (1989), 73–87 | MR | Zbl

[10] Olszak Z., Rosca R., “Normal locally conformal almost cosymplectic manifolds”, Publ. Math. Debrecen, 39:3–4 (1991), 315–323 | MR | Zbl