论文标题
在Chern的猜想上
On the Chern conjecture for isoparametric hypersurfaces
论文作者
论文摘要
对于封闭的高度表面$ m^n \子集s^{n+1}（1）$，具有恒定平均曲率和恒定的非负鳞片曲率，本文表明，如果$ \ sathrm {tr}（\ mathcal {\ mathcal {a}^k）$是$ k = 3，$ k = 3，\ ldots $ $ $ a $ $ a $ $ a $ a $ for MANS的常数是等级的。结果将de almeida和brito \ cite {db90}的定理以$ n = 3 $的形式推广到任何维度$ n $，从而强烈支持Chern的猜想。
For a closed hypersurface $M^n\subset S^{n+1}(1)$ with constant mean curvature and constant non-negative scalar curvature, the present paper shows that if $\mathrm{tr}(\mathcal{A}^k)$ are constants for $k=3,\ldots, n-1$ for shape operator $\mathcal{A}$, then $M$ is isoparametric. The result generalizes the theorem of de Almeida and Brito \cite{dB90} for $n=3$ to any dimension $n$, strongly supporting Chern's conjecture.
