On Deformable Hypersurfaces in Space Forms

被引：24

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
DAJCZER, M
GROMOLL, D
[J]. MATHEMATISCHE ZEITSCHRIFT, 1986, 191 (02) : 201 - 205
[9] ISOMETRIC DEFORMATIONS OF COMPACT EUCLIDEAN SUBMANIFOLDS IN CODIMENSION-2
DAJCZER, M
GROMOLL, D
[J]. DUKE MATHEMATICAL JOURNAL, 1995, 79 (03) : 605 - 618
[10] DAJCZER M, 1985, J DIFFER GEOM, V22, P13

← 1 2 3 →