Pinched Constantly Curved Holomorphic Two-Spheres in the Complex Grassmann Manifolds

Abstract

In the recent paper (Wang et al. in Differ Geom Appl 80:101840, 2022), the authors and Xu have established a Simons-type integral inequality for holomorphic curves in a complex Grassmann manifold G(k, N). In this paper, we completely classify holomorphic immersions from the two-sphere of constant curvature into G(3, N) with the norm of the second fundamental form satisfying the equality case of the inequality and prove that any such immersion can be decomposed as the “direct sum” of some “foundation stones” up to congruence.