球面中极小超曲面的Laplacian谱

THE SPECTRUM OF THE LAPLACIAN ON MINIMAL HYPERSURFACES IN A SPHERE

本文研究球面Ｓｎ＋１中与Ｃｌｉｆｏｒｄ超曲面等谱的某类极小超曲面，证明了如果此类超曲面的第二基本形式长度平方不小于ｎ，则它与Ｃｌｉｆｏｒｄ超曲面等距同构．

In this note we study the spectrum of Laplacian for some kind of minimal hypersurface in a sphere S n+1 which has the same spectrum as the Clifford hypersurface,and prove that if its square of the length of the second fundamental form is not less than n it is isometric to the Clifford hypersurface.