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Curves in a Grassmann Manifold

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

Abstract

As in §8 we will denote by Gr(N,k) the Grassmann manifold of all k-dimensional linear subspaces of the projective space PN of dimension N. Let M be a one-dimensional complex manifold or Riemann surface. A holomorphic curve in Gr(N,k) is a holomorphic mapping f: M → Gr(N,k). In particular, a holomorphic curve f: M → Gr(1,0) = P1, is a meromorphic function on M, given by the ratio of the homogeneous coordinates in P1.

Keywords

Riemann Surface Holomorphic Mapping Meromorphic Function Grassmann Manifold Holomorphic Curve 
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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Copyright information

© S.-s. Chern 1979

Authors and Affiliations

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

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