On holomorphic curves of constant curvature in the complex grassmann manifold G(2, 5)

In this article, it is proved that there doesn't exist any nonsingular holomorphic sphere in complex Grassmann manifold G(2,5) with constant curvature k = 4/7, 1/2, 4/9. Thus, from [7] it follows that if ϕ :S2 → G(2,5) is a nonsingular holomorphic curve with constant curvature K, then, K = 4,2,4/3, 1 or 4/5.