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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1979 S.-s. Chern
About this chapter
Cite this chapter
Chern, Ss. (1979). Curves in a Grassmann Manifold. In: Complex Manifolds without Potential Theory. Universitext. Springer, New York, NY. https://doi.org/10.1007/978-1-4684-9344-3_9
Download citation
DOI: https://doi.org/10.1007/978-1-4684-9344-3_9
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-90422-1
Online ISBN: 978-1-4684-9344-3
eBook Packages: Springer Book Archive