Geodesic
Vaisman–Gray manifolds with $J$-invariant
Sbornik. Mathematics, Tome 194 (2003) no. 2, pp. 225-235 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The class of Vaisman–Gray manifolds of dimension higher than 4 with $J$-invariant conformal curvature tensor is shown to coincide with the class of locally conformally nearly Kähler manifolds. Classifications of conformally flat and conformally para-Kähler Vaisman–Gray manifolds are obtained. 
@article{SM_2003_194_2_a2,
     author = {L. A. Ignatochkina},
     title = {Vaisman{\textendash}Gray manifolds with $J$-invariant},
     journal = {Sbornik. Mathematics},
     pages = {225--235},
     year = {2003},
     volume = {194},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2003_194_2_a2/}
}
TY  - JOUR
AU  - L. A. Ignatochkina
TI  - Vaisman–Gray manifolds with $J$-invariant
JO  - Sbornik. Mathematics
PY  - 2003
SP  - 225
EP  - 235
VL  - 194
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/SM_2003_194_2_a2/
LA  - en
ID  - SM_2003_194_2_a2
ER  - 
%0 Journal Article
%A L. A. Ignatochkina
%T Vaisman–Gray manifolds with $J$-invariant
%J Sbornik. Mathematics
%D 2003
%P 225-235
%V 194
%N 2
%U http://geodesic.mathdoc.fr/item/SM_2003_194_2_a2/
%G en
%F SM_2003_194_2_a2
L. A. Ignatochkina. Vaisman–Gray manifolds with $J$-invariant. Sbornik. Mathematics, Tome 194 (2003) no. 2, pp. 225-235. http://geodesic.mathdoc.fr/item/SM_2003_194_2_a2/

[1] Gray A., Hervella L. M., “The sixteen classes of almost Hermitian manifolds and their linear invariants”, Ann. Math. Pura Appl. (4), 123 (1980), 35–58 | DOI | MR | Zbl

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

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

[4] Gray A., Vanhecke L., “Almost Hermitian manifolds with constant holomorphic sectional curvature”, Cas. Pest. Mat., 104 (1979), 170–179 | MR | Zbl

[5] Kirichenko V. F., “Lokalno konformno-kelerovy mnogoobraziya postoyannoi golomorfnoi sektsionnoi krivizny”, Matem. sb., 182:3 (1991), 354–363 | MR | Zbl

[6] Kirichenko V. F., “Konformno ploskie lokalno konformno-kelerovy mnogoobraziya”, Matem. zametki, 51:5 (1992), 57–66 | MR | Zbl

[7] Kirichenko V. F., Ezhova N. A., “Konformnye invarianty mnogoobrazii Vaismana–Greya”, UMN, 51:2 (1996), 163–164 | MR | Zbl

[8] Gray A., “Curvature identities for Hermitian and almost Hermitian manifolds”, Tôhoku Math. J. (2), 28 (1976), 601–612 | DOI | MR | Zbl

[9] Vanhecke L., “Almost Hermitian manifolds with $J$-invariant Riemannian curvature tensor”, Rend. Sem. Math. Univ. Polilec. Torino, 34 (1975), 487–498 | MR

[10] Kirichenko V. F., “Differentsialnaya geometriya $K$-prostranstv”, Itogi nauki i tekhn. Problemy geometrii, 8, VINITI, M., 1977, 139–161

[11] Schipkova N. N., Differentsialnaya geometriya mnogoobrazii Vaismana–Greya, Diss. ... kand. fiz.-matem. nauk, MPGU, M., 1994

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

[13] Rashevskii P. K., Rimanova geometriya i tenzornyi analiz, Nauka, M., 1976

[14] Ignatochkina L. A., Kirichenko V. F., “Konformno-invariantnye svoistva priblizhenno kelerovykh mnogoobrazii”, Matem. zametki, 66:5 (1999), 653–663 | MR | Zbl

[15] Kobayasi Sh., Nomidzu K., Osnovy differentsialnoi geometrii, t. 1, 2, Nauka, M., 1981

[16] Rizza G. B., “Varieta parakähleriane”, Ann. Math. Pura Appl. (4), 98:4 (1974), 47–61 | DOI | MR | Zbl