On pseudo-holomorphic curves from two-spheres into a complex Grassmannian \(G(2,5)\) (Q966560)

The authors use harmonic sequences and the Kähler angle to discuss the curvature of pseudo-holomorphic curves from two-spheres \(S^2\) into a complex Grassmann manifold \(G(2,5)\). They study linearly full totally unramified pseudo-holomorphic curves \(s: S^2\to G(2,5)\) with constant Gaussian curvature \(K\), and, they prove: \(K\) is either \(\frac{1}{2}\) or \(\frac{4}{5}\) if \(s\) is non-\(\pm\)holomorphic with constant Gaussian curvature; \(K\) is \(\frac{1}{2}\) if and only if it is totally real; \(K\) is either \(1\) or \(\frac{4}{3}\) if \(s\) is a non-degenerate holomorphic curve of constant curvature under some conditions.