Local rigidity of holomorphic curves in the complex Grassmann manifold G(2,6)

In this paper, we first obtain the Gauss equation for the non-degenerate holomorphic immersions from a Riemann surface into the complex Grassmann manifold G(2,6). By using it, we prove that any two linearly full non-degenerate holomorphic curves in G(2,6) are congruent if they have the same first and second fundamental forms.