Curves in a Grassmann Manifold

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


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.


Riemann Surface Holomorphic Mapping Meromorphic Function Grassmann Manifold Holomorphic Curve 
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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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