S^n中Moebius形式平行的曲面

Surfaces with Parallel Moebius Forms in S^n

证明了如下结果:设x:M^2→S^n(n≥3)是不含脐点的曲面,若x的法丛平坦,则x的Moebius形式φ平行(φ=0)当且仅当φ4=0。

In this paper we prove the result that if x :M2→Sn(n≥3) is an umbilic-free surface with flat Moebius normal bundle then its Moebius form is parallel (▽φ=0) if and only if the Moebius form vanishes (φ=0).