Classification of holomorphic spheres of constant curvature in complex Grassmann manifold G2,5

In this paper, we classify all nonsingular holomorphic spheres in complex Grassmann manifolds G2,5 with the induced constant curvatures K=4, 2, 4/3,1 and 4/5 into some classes, up to unitary equivalence, in which none of the spheres are congruent; At the same time we also prove that there does not exist the nonsingular holomorphic sphere in G2,5 with constant curvature 2/3.