Almost complex manifold

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This article defines a differential manifold with the following additional structure -- the structure group is reduced to: general linear group over complex numbers

Definition

An almost complex manifold is the following data:

  • A differential manifold M
  • At each point, a complex structure to the vector space at that point. In other words, for every point, we give a linear map J such that J^2 = -I, with J varying smoothly with the point.

Relation with other structures

Stronger structures

Weaker structures