On conformal minimal 2-spheres in complex Grassmann manifold G(2,n)

Jie Fei, Xiaoxiang Jiao, Xiaowei Xu*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)

Abstract

For a harmonic map f from a Riemann surface into a complex Grassmann manifold, Chern and Wolfson [4] constructed new harmonic maps ∂ f and -∂ f through the fundamental collineations ∂ and -∂ respectively. In this paper, we study the linearly full conformal minimal immersions from S2 into complex Grassmannians G(2, n), according to the relationships between the images of ∂ f and -∂ f .We obtain various pinching theorems and existence theorems about the Gaussian curvature, Kähler angle associated to the given minimal immersions, and characterize some immersions under special conditions. Some examples are given to show that the hypotheses in our theorems are reasonable.

Original languageEnglish
Pages (from-to)181-199
Number of pages19
JournalProceedings of the Indian Academy of Sciences: Mathematical Sciences
Volume121
Issue number2
DOIs
Publication statusPublished - May 2011
Externally publishedYes

Keywords

  • Function of analytic type
  • Gaussian curvature
  • Kähler angle

Cite this