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In this paper, the theory of functions of one complex variable is explored tostudy linearly full unramified holomorphic two-spheres with constant curvaturein $G(2,n)$ satisfying that the generated harmonic sequence degenerates atposition $2$. Firstly, we determine the value distribution of the curvature andgive the explicit characterization of such holomorphic two-spheres in terms ofa polynomial equation. Then, applying this characterization, many examples ofnon-homogeneous constantly curved holomorphic two-spheres are constructed.

On holomorphic two-spheres with constant curvature in the complex Grassmann manifold G(2,n)