On holomorphic curves in a complex Grassmann manifold <Emphasis Type="Italic">G</Emphasis>(2, <Emphasis Type="Italic">n</Emphasis>)

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) = \frac4n-2{K(s) = \frac{4}{n-2}} if K(s) satisfies K(s) 3 \frac4n-2{K(s) \geq \frac{4}{n-2}} or K(s) ￡ \frac4n-2 {K(s) \leq \frac{4}{n-2} } everywhere on S ². In particular, K(s) = \frac4n-2{K(s) = \frac{4}{n-2}} if K(s) is constant.