On pseudo-holomorphic curves from two-spheres into a complex Grassmannian G(2, 5)

Abstract

Let s: S 2 → G(2, 5) be a linearly full totally unramified pseudo-holomorphic curve with constant Gaussian curvature K in a complex Grassmann manifold G(2, 5). It is prove that K is either 1/2 or 4/5 if s is non-±holomorphic. Furthermore, K = 1/2 if and only if s is totally real. We also prove that the Gaussian curvature K is either 1 or 4/3 if s is a non-degenerate holomorphic curve under some conditions.