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Archiv der Mathematik

, Volume 96, Issue 3, pp 291–300 | Cite as

On holomorphic curves in a complex Grassmann manifold G(2, n)

  • Xiaoxiang Jiao
  • Yan Yu
Article

Abstract

Let s : S 2G(2, n) be a linearly full totally unramified non-degenerate holomorphic curve in a complex Grassmann manifold G(2, n), and let K(s) be its Gaussian curvature. It is proved that \({K(s) = \frac{4}{n-2}}\) if K(s) satisfies \({K(s) \geq \frac{4}{n-2}}\) or \({K(s) \leq \frac{4}{n-2} }\) everywhere on S 2. In particular, \({K(s) = \frac{4}{n-2}}\) if K(s) is constant.

Mathematics Subject Classification (2010)

Primary 53C42 Secondary 53C55 

Keywords

Holomorphic Curves Harmonic Sequence Gaussian Curvature Pinching 

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Copyright information

© Springer Basel AG 2011

Authors and Affiliations

  1. 1.Department of MathematicsGraduate University, Chinese Academy of SciencesBeijingChina
  2. 2.College of SciencesNortheast Dianli UniversityJilin CityChina

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