Some Formulas Related to Complex Transgression

  • Raoul Bott
  • Shiing S. Chern

Abstract

Let X be a complex manifold of complex dimension n and π: E→X a holomorphic vector bundle whose fiber dimension is also n. On E we introduce a positive definite hermitian norm N and denote by B*(E) = {eϵE\0<N(e)} the subset of non-zero vectors of E. Let c n (E) be the Chern form of the hermitian structure (to be described again below).

Let X be a complex manifold of complex dimension n and π: E→X a holomorphic vector bundle whose fiber dimension is also n. On E we introduce a positive definite hermitian norm N and denote by B*(E) = {eϵE\0<N(e)} the subset of non-zero vectors of E. Let c n (E) be the Chern form of the hermitian structure (to be described again below).

Keywords

Complex Manifold Fiber Dimension Curvature Matrice Complex Vector Space Holomorphic Vector Bundle 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Bibliography

  1. [1]
    Bott, R., and S. Chern: Hermitian vector bundles and the equidistribution of the zeroes of their holomorphic sections. Acta Math. 114, 71–112 (1965).MathSciNetMATHCrossRefGoogle Scholar
  2. [2]
    Chern, S.: Complex manifolds without potential theory. Princeton: Van Nostrand 1967.MATHGoogle Scholar
  3. [3]
    Flanders, H.: Development of an extended exterior differential calculus. Transactions of American Mathematical Society 75, 311–326 (1953).MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin · Heidelberg 1970

Authors and Affiliations

  • Raoul Bott
  • Shiing S. Chern

There are no affiliations available

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