Examples of compact non-Kähler almost Kähler manifolds

Cordero, Luis A.; Fernández, M.; de León, Manuel

doi:10.1090/S0002-9939-1985-0801339-X

Examples of compact non-Kähler almost Kähler manifolds
HTML articles powered by AMS MathViewer

by Luis A. Cordero, M. Fernández and Manuel de León PDF

Proc. Amer. Math. Soc. 95 (1985), 280-286 Request permission

Abstract:

A parametrized family of compact non-Kähler almost Kähler manifolds ${M^{2r + 2}}$, $r \geqslant 1$, is constructed. For $r$ odd, these manifolds are shown to have odd first Betti number, so they cannot be Kählerian.

References

Elsa Abbena, An example of an almost Kähler manifold which is not Kählerian, Boll. Un. Mat. Ital. A (6) 3 (1984), no. 3, 383–392 (English, with Italian summary). MR 769169
Louis Auslander, The structure of complete locally affine manifolds, Topology 3 (1964), no. suppl, suppl. 1, 131–139. MR 161255, DOI 10.1016/0040-9383(64)90012-6
Samuel I. Goldberg, Curvature and homology, Pure and Applied Mathematics, Vol. XI, Academic Press, New York-London, 1962. MR 0139098
Alfred Gray, Curvature identities for Hermitian and almost Hermitian manifolds, Tohoku Math. J. (2) 28 (1976), no. 4, 601–612. MR 436054, DOI 10.2748/tmj/1178240746
Alfred Gray, Homogeneous almost Hermitian manifolds, Rend. Sem. Mat. Univ. Politec. Torino Special Issue (1983), 17–58 (1984). Conference on differential geometry on homogeneous spaces (Turin, 1983). MR 828996

Sur une généralisation des structures de contact

Shoshichi Kobayashi and Katsumi Nomizu, Foundations of differential geometry. Vol I, Interscience Publishers (a division of John Wiley & Sons, Inc.), New York-London, 1963. MR 0152974
John Milnor, Curvatures of left invariant metrics on Lie groups, Advances in Math. 21 (1976), no. 3, 293–329. MR 425012, DOI 10.1016/S0001-8708(76)80002-3
W. P. Thurston, Some simple examples of symplectic manifolds, Proc. Amer. Math. Soc. 55 (1976), no. 2, 467–468. MR 402764, DOI 10.1090/S0002-9939-1976-0402764-6
Bill Watson, New examples of strictly almost Kähler manifolds, Proc. Amer. Math. Soc. 88 (1983), no. 3, 541–544. MR 699430, DOI 10.1090/S0002-9939-1983-0699430-2