The Newlander-Nirenberg theorem states that any Integrable Almost Complex manifold is a complex manifold. I am looking for natural examples of complex structures that are not integrable.
Nonintegrable almost complex structures
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geometry
differential-geometry
complex-geometry
almost-complex
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0I changed the title by adding "almost", because *nonintegrable complex structure* is an oxymoron. Also, I added some relevant tags. – 2011-06-23