V. Apostolov and J. Armstrong, Symplectic 4-manifolds with Hermitian Weyl tensor, Transactions of the American Mathematical Society, vol.352, issue.10, pp.4501-4513, 2000.
DOI : 10.1090/S0002-9947-00-02624-6

V. Apostolov, J. Armstrong, and T. Draghici, Local rigidity of certain classes of almost Kähler 4-manifolds, math, p.9911197

V. Apostolov, T. Draghici, and A. Moroianu, A SPLITTING THEOREM FOR K??HLER MANIFOLDS WHOSE RICCI TENSORS HAVE CONSTANT EIGENVALUES, International Journal of Mathematics, vol.12, issue.07, pp.769-789, 2001.
DOI : 10.1142/S0129167X01001052

J. Armstrong, An Ansatz for Almost-Kähler, Einstein 4-manifolds, to appear in J. reine angew

D. E. Blair and S. Ianus, Critical associated metrics on symplectic manifolds, Contemp. Math, vol.51, pp.23-29, 1986.
DOI : 10.1090/conm/051/848929

J. Bourguignon, Les vari???t???s de dimension 4 ??? signature non nulle dont la courbure est harmonique sont d'Einstein, Inventiones Mathematicae, vol.74, issue.2, pp.263-286, 1981.
DOI : 10.1007/BF01393878

J. Davidov and O. , Mu? skarov, Twistor spaces with Hermitian Ricci tensor, Proc. Amer, pp.1115-1120, 1990.

T. Draghici, Almost Kähler 4-manifolds with J-invariant Ricci tensor, Houston J. Math, vol.25, pp.133-145, 1999.

. Th and . Friedrich, The Classification of 4?dimensional Kähler Manifolds with Small Eigenvalue of the Dirac Operator, Math. Ann, vol.295, pp.565-574, 1993.

]. S. Gallot, ??quations diff??rentielles caract??ristiques de la sph??re, Annales scientifiques de l'??cole normale sup??rieure, vol.12, issue.2, pp.235-267, 1979.
DOI : 10.24033/asens.1366

S. I. Goldberg, Integrability of almost Kaehler manifolds, Proc. Amer, pp.96-100, 1969.
DOI : 10.1090/S0002-9939-1969-0238238-1

A. Gray, Curvature identities for Hermitian and almost Hermitian manifolds, Tôhoku Math, J, vol.28, pp.601-612, 1976.
DOI : 10.2748/tmj/1178240746

URL : http://projecteuclid.org/download/pdf_1/euclid.tmj/1178240746

K. and ?. D. Kirchberg, The first eigenvalue of the Dirac operator on K??hler manifolds, Journal of Geometry and Physics, vol.7, issue.4, pp.449-468, 1990.
DOI : 10.1016/0393-0440(90)90001-J

S. Kobayashi, On Compact Kahler Manifolds with Positive Definite Ricci Tensor, The Annals of Mathematics, vol.74, issue.3, pp.570-574, 1961.
DOI : 10.2307/1970298

A. Moroianu, On Kirchberg inequality for compact Kähler manifolds of even complex dimension, Annals of Global Analysis and Geometry, vol.15, issue.3, pp.235-242, 1997.
DOI : 10.1023/A:1006543304443

A. Moroianu, Parallel and Killing Spinors on Spin c Manifolds, Communications in Mathematical Physics, vol.187, issue.2, pp.417-428, 1997.
DOI : 10.1007/s002200050142

URL : https://hal.archives-ouvertes.fr/hal-00125985

A. Moroianu, Kähler manifolds with small eigenvalues of the Dirac operator and a conjecture of Lichnerowicz, Ann. Inst. Fourier (Grenoble), pp.49-1637, 1999.

T. Oguro and K. Sekigawa, Four-dimensional almost Kähler Einstein and * -Einstein manifolds, Geom. Dedicata, pp.69-91, 1998.

K. Sekigawa, On some compact Einstein almost K??hler manifolds, Journal of the Mathematical Society of Japan, vol.39, issue.4, pp.677-684, 1987.
DOI : 10.2969/jmsj/03940677

F. Tricerri and L. Vanhecke, Curvature tensors on almost Hermitian manifolds, Transactions of the American Mathematical Society, vol.267, issue.2, pp.365-398, 1981.
DOI : 10.1090/S0002-9947-1981-0626479-0