Geodesic
Locally conformallity Kählerian manifolds of constant holomorphic sectional curvature
Sbornik. Mathematics, Tome 72 (1992) no. 2, pp. 333-342 
V. F. Kirichenko. Locally conformallity Kählerian manifolds of constant holomorphic sectional curvature. Sbornik. Mathematics, Tome 72 (1992) no. 2, pp. 333-342. http://geodesic.mathdoc.fr/item/SM_1992_72_2_a2/
@article{SM_1992_72_2_a2,
     author = {V. F. Kirichenko},
     title = {Locally conformallity {K\"ahlerian} manifolds of constant holomorphic sectional curvature},
     journal = {Sbornik. Mathematics},
     pages = {333--342},
     year = {1992},
     volume = {72},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1992_72_2_a2/}
}
TY  - JOUR
AU  - V. F. Kirichenko
TI  - Locally conformallity Kählerian manifolds of constant holomorphic sectional curvature
JO  - Sbornik. Mathematics
PY  - 1992
SP  - 333
EP  - 342
VL  - 72
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/SM_1992_72_2_a2/
LA  - en
ID  - SM_1992_72_2_a2
ER  - 
%0 Journal Article
%A V. F. Kirichenko
%T Locally conformallity Kählerian manifolds of constant holomorphic sectional curvature
%J Sbornik. Mathematics
%D 1992
%P 333-342
%V 72
%N 2
%U http://geodesic.mathdoc.fr/item/SM_1992_72_2_a2/
%G en
%F SM_1992_72_2_a2

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

The author studies the structure of the curvature tensor of $L\mathscr C$-manifolds, i.e., almost Hermitian manifolds whose metric is, at least locally, conformally related to a Kählerian metric (with the same structure operator).

[1] Hawley N. S., “Constant holomorphic curvature”, Canad. J. Math., 5:1 (1953), 53–56 | MR | Zbl

[2] Igusa J., “On the structure of a certain class of Hähler varietes”, Amer. J. Math., 76:3 (1954), 669–678 | DOI | MR | Zbl

[3] Gray A., “Classification des varietes approximativement kähleriennes de courbure sectionelle holomorphe constante”, C. r. Acad. sci., 279:22 (1974), 797–800 | MR | Zbl

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

[5] Naveira A., Hervella L., “Shur's theorem for nearly Hähler manifolds”, Proc. Amer. Math. Soc., 49:2 (1975), 421–425 | DOI | MR | Zbl

[6] Gray A., Vanhecke L., “Almost Hermitian manifolds with constant holomorphic sectional curvature”, Cas. pestov. mat., 104:2 (1979), 170–179 | MR | Zbl

[7] Gray A., Hervella L., “The sixteen classes of almost Hermitian manifolds and their linear invariants”, Ann. Math. pure ed appl., 128:4 (1980), 35–58 | DOI | MR

[8] Vaisman I., “On locally and globally conformal Kähler manifolds”, Trans. Amer. Math. Soc., 262 (1980), 533–542 | DOI | MR | Zbl

[9] Vaisman I., “Locally conformal Hähler manifolds with parallel Lee forms”, Rend. di Mat., 12 (1979), 268–284 | MR

[10] Kirichenko V. F., “Kvaziodnorodnye mnogoobraziya i obobschennye pochti ermitovy struktury”, Izv. AN SSSR. Ser. matem., 47:6 (1984), 1208–1223 | MR

[11] Kirichenko V. F., “Metody obobschennoi ermitovoi geometrii v teorii pochti kontaktnykh mnogoobrazii”, Probl. geometrii, Itogi nauki i tekhn., 18, 1986, 25–72 | MR

[12] Kobayasi Sh., Nomidzu K., Osnovy differentsialnoi geometrii, t. 1, Nauka, M., 1981

[13] Gray A., “Curvature identities for Hermitian and almost Hermitian manifolds”, Tohoku Math. J., 28:4 (1976), 601–612 | DOI | MR | Zbl

[14] Vaisman I., “Some curvature properties of locally conformal Hähler manifolds”, Trans. Amer. Math. Soc., 259:2 (1980), 439–447 | DOI | MR | Zbl

[15] Myers S. B., “Riemannian manifolds in the large”, Duke Math. J., 1 (1935), 39–49 | DOI | MR | Zbl

[16] Vanhecke L., “Almost Hermitian manifolds with $J$-invariant Riemannian curvature tensor”, Rend. semin. mat. Univ. e politecn. Torino, 34 (1975–1976), 487–498 | MR

[17] Nagano T., “The conformal transformation on a space with parallel Ricci tensor”, J. Math. Soc. Japan, 11 (1959), 10–14 | MR | Zbl