论文标题
离散类中Sbrana-Cartan Hypersurfaces的结构
A construction of Sbrana-Cartan hypersurfaces in the discrete class
论文作者
论文摘要
U. Sbrana在1909年获得的局部异端变形的欧几里得高度曲面的经典分类和1916年的E. Cartan包括四个类别，其中包括Submanifolds形成的类别，仅允许单个变形。实际上，这些SBRANA-CARTAN HYPERFACES是否存在的问题均未由任何一个都解决。 Dajczer-florit-tojeiro在1998年给出了对这个问题的积极答案，该问题称为双曲线类型，而Dajczer-florit在2004年是椭圆类型，这是另一种可能性。在这两种情况下，构建的示例都是非常特别的。本文的主要结果产生了许多类型的超曲面的示例，并且似乎指向分类的方向，尽管该目标仍然难以捉摸。
The classical classifications of the locally isometrically deformable Euclidean hypersurfaces obtained by U. Sbrana in 1909 and E. Cartan in 1916 includes four classes, among them the one formed by submanifolds that allow just a single deformation. The question of whether these Sbrana-Cartan hypersurfaces do, in fact, exist was not addressed by either of them. Positive answers to this question were given by Dajczer-Florit-Tojeiro in 1998 for the ones called of hyperbolic type and by Dajczer-Florit in 2004 when of elliptic type which is the other possibility. In both cases the examples constructed are rather special. The main result of this paper yields an abundance of examples of hypersurfaces of either type and seems to point in the direction of a classification although that goal remains elusive.
