On holomorphic curves in a complex Grassmann manifold G(2, n)

摘要

Let s: S~2 → G(2, n) be a linearly full totally unramified non-degenerate holomorphic curve in a complex Grassmann manifold G(2, n), and let K(s) be its Gaussian curvature. It is proved that K(s)= 4-2 if K(s) satisfies K(s)≥ 4-2 or K(s)≤ 4-2 everywhere on S~2. In particular, K(s)= 4-2 if K(s) is constant.