Almost Complex Manifolds; Integrability Conditions
Let M be a C∞ manifold of dimension n. To a point x ∈ M we will denote by Tx and T x * the tangent and cotangent spaces respectively. An almost complex structure on M is a C∞ field of endomorphisms Jx: Tx → Tx, such that J x 2 = −1x, where 1x denotes the identity endomorphism in Tx.
KeywordsComplex Manifold Integrability Condition Local Coordinate System Tensor Field Cotangent Space
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