论文标题
较高的包装中欧几里得高曲面的真正变形i
Genuine deformations of Euclidean hypersurfaces in higher codimensions I
论文作者
论文摘要
SBRANA和CARTAN为欧几里得高空外面提供了本地分类，$ m^n \ subseteq \ mathbb {r}^{n+1} $，该{n+1} $允许另一个真正的等距浸入$ \ mathbb {r}^r}^{n+1} $ n \ n \ geq 3 $中。本文的主要目的是将其分类扩展到更高的编码。我们的主要结果是对$ \ Mathbb {r}^{r}^{n+p} $ in Cark $（p+1）$的真实变形的模量空间的完整描述。 As a consequence, we obtain an analogous classification to the ones given by Sbrana and Cartan providing all local isometric immersions in $\mathbb{R}^{n+2}$ of a generic hypersurface $M^n\subseteq\mathbb{R}^{n+1}$ for $n\geq 4$.我们还展示了此处开发的技术如何用于研究纯净的欧几里得亚曼叶。
Sbrana and Cartan gave local classifications for the set of Euclidean hypersurfaces $M^n\subseteq\mathbb{R}^{n+1}$ which admit another genuine isometric immersions in $\mathbb{R}^{n+1}$ for $n\geq 3$. The main goal of this paper is to extend their classification to higher codimensions. Our main result is a complete description of the moduli space of genuine deformations of generic hypersurfaces of rank $(p+1)$ in $\mathbb{R}^{n+p}$ for $p\leq n-2$. As a consequence, we obtain an analogous classification to the ones given by Sbrana and Cartan providing all local isometric immersions in $\mathbb{R}^{n+2}$ of a generic hypersurface $M^n\subseteq\mathbb{R}^{n+1}$ for $n\geq 4$. We also show how the techniques developed here can be used to study conformally flat Euclidean submanifolds.
