nLab Newlander-Nirenberg theorem

Idea

The Newlander-Nirenberg theorem states that an almost complex structure comes from a complex structure precisely if its Nijenhuis tensor vanishes.

For discussion of this in terms of integrability of G-structures see there at Examples – Complex structure.

Related concepts

• Koszul-Malgrange theorem

References

Textbook accounts include

• Claire Voisin, section 2.3.3 of Hodge theory and Complex algebraic geometry I,II, Cambridge Stud. in Adv. Math. 76, 77, 2002/3

Reviews include

• Ben McMillan, The Newlander-Nirenbeg theorem (pdf)