On Deformable Hypersurfaces in Space Forms

被引：23
|
作者：
Dajczer, M. [1 ]
Florit, L. [1 ]
Tojeiro, R. [2 ]
机构：
[1] IMPA, Estrada Dona Castorina 110, BR-22460320 Rio De Janeiro, RJ, Brazil
[2] Univ Fed Uberlandia, Uberlandia, MG, Brazil
来源：
ANNALI DI MATEMATICA PURA ED APPLICATA | 1998年 / 174卷 / 01期
关键词：
Large Family; Space Form; Hyperbolic Space; Unique Deformation; Euclidean Hypersurface;
D O I：
10.1007/BF01759378
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We first extend the classical Sbrana-Cartan theory of isometrically deformable euclidean hypersurfaces to the sphere and hyperbolic space. Then we construct and characterize a large family of hypersurfaces which admit a unique deformation. This is used to show, by means of explicit examples, that different types of hypersurfaces in the Sbrana-Cartan classification can be smoothly attached. Finally, among other applications, we discuss the existence of complete deformable hypersurfaces in hyperbolic space.
引用
收藏
页码：361 / 390
页数：30
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