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https://www.ias.ac.in/article/fulltext/pmsc/121/02/0181-0199

Gaussian curvature; Kähler angle; function of analytic type.

For a harmonic map 𝑓 from a Riemann surface into a complex Grassmann manifold, Chern and Wolfson [4] constructed new harmonic maps $\partial f$ and $\overline{\partial} f$ through the fundamental collineations 𝜕 and $\overline{\partial}$ respectively. In this paper, we study the linearly full conformal minimal immersions from $S^2$ into complex Grassmannians $G(2,n)$, according to the relationships between the images of $\partial f$ and $\overline{\partial}f$. 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.

Jie Fei¹ Xiaoxiang Jiao¹ Xiaowei Xu²

1. School of Mathematical Sciences, Graduate University of Chinese Academy of Sciences, Beijing 100049, People’s Republic of China
2. Department of Mathematics, University of Science and Technology of China, Hefei, Anhui 230026, People’s Republic of China

Published

May 2011

Manuscript received

2 August 2009

Manuscript revised

12 December 2010