Minimal two-spheres with constant curvature in the complex Grassmannians

Abstract

In this paper we use the Cartan embedding and the method of moving frames to study the geometry of 2-dimensional SU(2)-orbits in the complex Grassmann manifold G(k, n), and we express their geometric quantities explicitly. We obtain various minimal two-spheres in G(k, n) with constant curvature by studying the 2-dimensional orbits.