Almost Complex Manifolds; Integrability Conditions

  • Shiing-shen Chern
Part of the Universitext book series (UTX)


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.


Complex Manifold Integrability Condition Local Coordinate System Tensor Field Cotangent Space 
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Copyright information

© S.-s. Chern 1979

Authors and Affiliations

  • Shiing-shen Chern
    • 1
  1. 1.Department of MathematicsUniversity of CaliforniaBerkeleyUSA

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