A Characterization of Homogeneous Holomorphic Two-Spheres in Q_n

In this paper, we classify holomorphic curves in Q_n with certain geometric conditions. We study the (1,0) part of kth covariant derivative about the second fundamental form denoted by a_,k, 0≤k≤[n2]-2; the norm of its symmetric product is denoted by τ_k= | a_,k· a_,k|. It is proven that a holomorphic curve in Q_n is homogeneous if the Gaussian curvature, the norm of the second fundamental form and τ_k are all constant. Moreover, all the homogeneous holomorphic curves are uniquely determined by our given examples, up to a rigid motion of Q_n.