Minimal Surfaces In Grassmann Manifold

This paper introduces a generalized Frenet formula for holomorphic 2-spheres S² in Grassmann manifolds G(k,n) and gains a generalized Plu|¨cker formula. By use of these formulas a complete classification of constant curved holomorphic S² in G(2,4) is given. Some pinching theorems for Gaussian curvature generalizes the corresponding results about holomorphic and minimal S² in CP^n-1. Einsteinian holomorphic subbundle o(?) the trivial bundle S² × Cⁿ is investigated.