Geodesic
Geometry of the Conharmonic Curvature Tensor of Almost Hermitian Manifolds
Matematičeskie zametki, Tome 90 (2011) no. 1, pp. 87-103.

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

We obtain a criterion for manifolds of dimension $4$ and greater to be conharmonically para-Kähler and the condition for a manifold to be conharmonically flat.
Keywords: almost Hermitian manifold, Riemannian structure, conharmonic curvature tensor, Kähler manifold, para-Kähler manifold, Riemannian metric, nearly Kähler structure, Riemannian curvature, Ricci tensor.
Mots-clés : $G$-structure 
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V. F. Kirichenko; A. R. Rustanov; A. A. Shikhab. Geometry of the Conharmonic Curvature Tensor of Almost Hermitian Manifolds. Matematičeskie zametki, Tome 90 (2011) no. 1, pp. 87-103. http://geodesic.mathdoc.fr/item/MZM_2011_90_1_a8/

[1] Y. Ishii, “On conharmonic transformations”, Tensor (N.S.), 7:2 (1957), 73–80 | MR | Zbl

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

[3] L. Vanhecke, “Almost Hermitian manifolds with $J$-invariant Riemann curvature tensor”, Rend. Sem. Mat. Univ. Politec. Torino, 34 (1975/76), 487–498 | MR | Zbl

[4] A. Gray, “Six dimensional almost complex manifolds defined by means of three-fold vector cross products”, Tôhoku Math. J. (2), 21:4 (1969), 614–620 | DOI | MR | Zbl

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

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

[7] A. Gray, “The structures of nearly Kähler manifolds”, Math. Ann., 223:3 (1976), 233–248 | DOI | MR | Zbl

[8] M. Barros, A. Ramírez, “Decomposition of quasi-Kähler manifolds which satisfy the first curvature condition”, Demonstratio Math., 11:3 (1978), 685–694 | MR | Zbl

[9] S. Sawaki, K. Sekigawa, “Almost Hermitian manifolds with constant holomorphic sectional curvature”, J. Differential Geometry, 9 (1974), 123–134 | MR | Zbl

[10] G. B. Rizza, “Varietá parakähleriane”, Ann. Mat. Pura Appl. (4), 98:1 (1974), 47–61 | DOI | MR | Zbl

[11] L. Vanhecke, “Some almost Hermitian manifolds with constant holomorphic sectional curvature”, J. Differential Geometry, 12:4 (1977), 461–471 | MR | Zbl

[12] A. M. Naveira, L. M. Hervella, Quasi-Kähler manifolds, Preprint, 1975

[13] A. Gray, L. Vanhecke, “Almost Hermitian manifolds with constant holomorphic sectional curvature”, Časopis Pěst. Mat., 104:2 (1979), 170–179 | MR | Zbl

[14] B. Watson, L. Vanhecke, “$K_{1}$-curvatures and almost Hermitian submersions”, Rend. Sem. Mat. Univ. Politec. Torino, 36 (1977/78), 205–224 | MR | Zbl

[15] V. F. Kirichenko, “Generalized quasi-Kaehlerian manifolds and axioms of $CR$-submanifolds in generalized Hermitian geometry, II”, Geom. Dedicata, 52:1 (1994), 53–85 | DOI | MR | Zbl