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Is there any comprehensive reference for Almos-Kahler geometry or more generally to Almost- Hermitian geometry ?

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I added some more tags. I know 'complex geometry' is not strictly speaking appropriate here, but people who approach complex geometry from the differential-geometric viewpoint (such as me) are interested in almost Kahler manifolds or in almost Hermitian manifolds in general. – Spiro Karigiannis Mar 9 '11 at 14:57
Thanks for your appropriate remark. – Hamed Mar 9 '11 at 15:13

The paper that started this all is the one by Gray and Hervella where they classified the different types of almost Hermitian structures. It's a classic and still very much well worth reading:

The sixteen classes of almost Hermitian manifolds and their linear invariants.

A Gray, LM Hervella.

Ann. Mat. Pura Appl. (4) (1980) vol. 123 pp. 35-58

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Thank you for your help. Now I understood what I want to study. – Hamed Mar 9 '11 at 15:09

A slightly more current paper can be found here:

Apostolov, Vestislav; Drăghici, Tedi The curvature and the integrability of almost-Kähler manifolds: a survey. Symplectic and contact topology: interactions and perspectives (Toronto, ON/Montreal, QC, 2001), 25–53, Fields Inst. Commun., 35, Amer. Math. Soc., Providence, RI, 2003.

This gives a review of the various approaches to Almost Kaehler Geometry that has been taken since the Gray/Hervella article.

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Thanks Berndan. Those are really worth to study. – Hamed Aug 8 '13 at 19:13

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