A generalized Frenet formula for holomorphic 2-spheresS 2 in Grassmann manifoldsG(k,n) is introduced and a generalized Pliicker formula is achieved. By use of these formulae some pinching theorems for Gaussian curvatu...A generalized Frenet formula for holomorphic 2-spheresS 2 in Grassmann manifoldsG(k,n) is introduced and a generalized Pliicker formula is achieved. By use of these formulae some pinching theorems for Gaussian curvature are obtained which generalize the corresponding results about holomorphic and minimalS 2 inCP n-1. Einsteinian holomorphic subbundle of the trivial bundleS 2 ×C n is investigated.展开更多
文摘A generalized Frenet formula for holomorphic 2-spheresS 2 in Grassmann manifoldsG(k,n) is introduced and a generalized Pliicker formula is achieved. By use of these formulae some pinching theorems for Gaussian curvature are obtained which generalize the corresponding results about holomorphic and minimalS 2 inCP n-1. Einsteinian holomorphic subbundle of the trivial bundleS 2 ×C n is investigated.
