On Conformal Minimal 2-Spheres in Complex Grassmann Manifold 𝐺(2,𝑛)

Proceedings Mathematical Sciences

Xiaowei Xu¹  Jie Fei³  Xiaoxiang Jiao² 

[1] $$;Department of Mathematics, University of Science and Technology of China, Hefei, Anhui 00, People’s Republic of China$$;School of Mathematical Sciences, Graduate University of Chinese Academy of Sciences, Beijing 000, People’s Republic of China$$

关键词: Gaussian curvature;    Kähler angle;    function of analytic type.;   

DOI  :  

学科分类：数学（综合）

来源: Indian Academy of Sciences

【 摘 要 】

For a harmonic map 𝑓 from a Riemann surface into a complex Grassmann manifold, Chern and Wolfson [4] constructed new harmonic maps 𝜕 𝑓 and $overline{𝜕} f$ through the fundamental collineations 𝜕 and $overline{𝜕}$ 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 𝜕 𝑓 and $overline{𝜕}f$. 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.

【 授权许可】

Unknown