On Deformable Hypersurfaces in Space Forms

被引：25

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

页码：361 / 390

页数：30

共 21 条

[1]

Bianchi L, 1905, MEM SOC IT SC, VXIII, P261

[2]

BIANCHI L, 1930, LEZIONI GEOMETERIA D, V2

[3]

Bompiani E, 1917, CR HEBD ACAD SCI, V164, P508

[4]

BOMPIANI E, 1915, REND ACCAD LINCEI, V24, P126

[5]

Cartan E, 1916, B SOC MATH FRANCE, V44, P65

[6]

CARTAN E., 1917, B SOC MATH FRANCE, V44, P57

[7]

DAJCZER M, 1985, J DIFFER GEOM, V22, P1

[8] EUCLIDEAN HYPERSURFACES WITH ISOMETRIC GAUSS MAPS [J].

DAJCZER, M ;

GROMOLL, D .

MATHEMATISCHE ZEITSCHRIFT, 1986, 191 (02) :201-205

[9] ISOMETRIC DEFORMATIONS OF COMPACT EUCLIDEAN SUBMANIFOLDS IN CODIMENSION-2 [J].

DAJCZER, M ;

GROMOLL, D .

DUKE MATHEMATICAL JOURNAL, 1995, 79 (03) :605-618

[10]

DAJCZER M, 1985, J DIFFER GEOM, V22, P13

← 1 2 3 →