The Riemannian Geometry of Superminimal Surfaces in Complex Space Forms

<正> This paper deals with superminimal surfaces in complex space forms by using theFrenet framing. We formulate explicitly the length squares of the higher fundamental forms andthe higher curvatures for superminimal surfaces in terms of the metric of the surface and the Khlerangle of the immersion. Particularly, some curvature pinching theorems for minimal 2-spheres in acomplex projective space are given and a new characterization of the Veronese sequence is obtained.