اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدOn the Chern conjecture for isoparametric hypersurfaces
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For a closed hypersurface $M^nsubset S^{n+1}(1)$ 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 Cherns conjecture.
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