S + n+1 $\mbox{${\mathbb {S}}$}^{n+1}_+$中紧嵌入超曲面的同余定理

IF 1 3区数学 Q2 MATHEMATICS Bulletin of the London Mathematical Society Pub Date : 2025-01-22 DOI:10.1112/blms.70004

Allan Freitas, Felippe Guimarães

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引用次数: 0

摘要

我们证明了S + n+p $\mbox{${\mathbb {S}}$}^{n+p}$的紧n$ n$维子流形的一个协维约简和同余定理，它允许一个平均凸等距嵌入到S +中n+1 $\mbox{${\mathbb {S}}$}^{n+1}_+$使用赖利类型公式的空间形式。

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A congruence theorem for compact embedded hypersurfaces in S + n + 1 $\mbox{${\mathbb {S}}$}^{n+1}_+$

We prove a codimension reduction and congruence theorem for compact $n$ -dimensional submanifolds of $S^{n + p}$ that admit a mean convex isometric embedding into $S_{+}^{n + 1}$ using a Reilly-type formula for space forms.