Conformal infinitesimal variations of submanifolds

被引：1

作者：

Dajczer, Marcos ^{[1
]}

Jimenez, Miguel Ibieta ^{[2
]}

机构：

[1] IMPA, Estr Dona Castorina 110, BR-22460320 Rio De Janeiro, Brazil

[2] Univ Sao Paulo, Inst Ciencias Matemat & Comp, BR-13560970 Sao Carlos, SP, Brazil

来源：

DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS | 2021年 / 75卷

关键词：

Euclidean submanifolds; Conformal infinitesimal variations; Conformal infinitesimal bendings;

D O I：

10.1016/j.difgeo.2021.101721

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper belongs to the realm of conformal geometry and deals with Euclidean submanifolds that admit smooth variations that are infinitesimally conformal. Conformal variations of Euclidean submanifolds are a classical subject in differential geometry. In fact, already in 1917 Cartan classified parametrically the Euclidean hypersurfaces that admit nontrivial conformal variations. Our first main result is a Fundamental theorem for conformal infinitesimal variations. The second is a rigidity theorem for Euclidean submanifolds that lie in low codimension. (c) 2021 Elsevier B.V. All rights reserved.

引用

页数：21

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