关于球面上极小子流形的一点注记

A Remark on Minimal Submanifolds in a Sphere

本文沿用[2]的方法,把球面上紧致极小子流形纯量曲率的拚挤常数改进为n^2-4n(2n+1)/(5n+2).

By the method of [2], we improve a result of [2] as follows : Theorem Let Sn+p be a unit (n+p)-sphere and Mn→Sn+p (n≥2) be compact minimal submanifold of Sn+p. If R≥n2-4n(2n + 1)/(5n + 2) or equivalently ||σ||2≤n(3n + 2)/(5n + 2), where R and ||σ||2 are the scalar curvature and the length square of thesecond fundamental form of Mn, respectively, then either Mn is totally geodesic or n=2 and M2 is the Feronese surface in S4.