Introduction and Examples

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


A complex manifold is a paracompact Hausdorff space which has a covering by neighborhoods each homeomorphic to an open set in the m-dimensional complex number space such that where two neighborhoods overlap the local coordinates transform by a complex analytic transformation. That is, if z1,..., zm are local coordinates in one such neighborhood and if w1,..., wm are local coordinates in another neighborhood, then where they are both defined, we have wi = wi (z1,..., zm), where each wi is a holomorphic (or analytic) function of the z’s and the functional determinant ∂(w1,..., wm)/∂(z1,..., zm) 0.


Line Bundle Holomorphic Function Complex Manifold Functional Determinant Gaussian Integer 
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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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