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

Abstract

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 \(\bar{\partial}\!f\) through the fundamental collineations \(\partial\) and \(\bar{\partial}\) 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 \(\partial\!f\) and \(\bar{\partial}\!f\). We obtain various pinching theorems and existence theorems about the Gaussian curvature, Kahler 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.