On isometric and conformal rigidity of submanifolds

被引：5

作者：

Silva, SL ^{[1
]}

机构：

[1] Univ Estadual Rio de Janeiro, Dept Estruturas Matemat, IME, BR-20550013 Rio De Janeiro, Brazil

来源：

PACIFIC JOURNAL OF MATHEMATICS | 2001年 / 199卷 / 01期

关键词：

D O I：

10.2140/pjm.2001.199.227

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this article we introduce a new conformal invariant and we prove a conformal rigidity theorem which has no restriction on the size of the codimension. We also prove an isometric rigidity theorem whose assumptions are less restrictive than in Allendoerfer's theorem.

引用

页码：227 / 247

页数：21

共 50 条

[31] Isometric Rigidity in Codimension 2 [J].

Dajczer, Marcos ;

Morais, Pedro .

MICHIGAN MATHEMATICAL JOURNAL, 2009, 58 (03) :759-770

[32] A general rigidity theorem for complete submanifolds [J].

Shiohama, K ;

Xu, HW .

NAGOYA MATHEMATICAL JOURNAL, 1998, 150 :105-134

[33] RIGIDITY FOR ELLIPTIC ISOMETRIC IMBEDDINGS [J].

TANAKA, N .

PROCEEDINGS OF THE JAPAN ACADEMY, 1972, 48 (06) :370-&

[34] INTRINSIC RIGIDITY FOR COMPACT MINIMAL SUBMANIFOLDS [J].

沈一兵 .

ScienceBulletin, 1988, (06) :523-524

[35] RIGIDITY OF IMMERSED SUBMANIFOLDS IN A HYPERBOLIC SPACE [J].

Nguyen Thac Dung .

Bulletin of the Korean Mathematical Society, 2016, 53 (06) :1795-1804

[36] ON INTRINSIC RIGIDITY FOR MINIMAL SUBMANIFOLDS IN A SPHERE [J].

沈一兵 .

Science China Mathematics, 1989, (07) :769-781

[37] Geometric and differentiable rigidity of submanifolds in spheres [J].

Xu, Hongwei ;

Huang, Fei ;

Zhao, Entao .

JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, 2013, 99 (03) :330-342

[38] ON MASLOV CLASS RIGIDITY FOR COISOTROPIC SUBMANIFOLDS [J].

Ginzburg, Viktor L. .

PACIFIC JOURNAL OF MATHEMATICS, 2011, 250 (01) :139-161

[39] Torsional rigidity of submanifolds with controlled geometry [J].

Hurtado, A. ;

Markvorsen, S. ;

Palmer, V. .

MATHEMATISCHE ANNALEN, 2009, 344 (03) :511-542

[40] Rigidity of submanifolds in the Euclidean and spherical spaces [J].

da Silva, Jonatan F. ;

de Lima, Henrique F. ;

dos Santos, Fabio R. ;

Velasquez, Marco Antonio L. .

RENDICONTI DEL CIRCOLO MATEMATICO DI PALERMO, 2020, 69 (01) :159-165

← 1 2 3 4 5 →