Infinitesimal Variations of Submanifolds

被引：0

作者：

Marcos Dajczer

Miguel Ibieta Jimenez

机构：

[1] IMPA – Estrada Dona Castorina,Instituto de Ciências Matemáticas e de Computação

[2] 110,undefined

[3] Universidade de São Paulo,undefined

来源：

Bulletin of the Brazilian Mathematical Society, New Series | 2021年 / 52卷

关键词：

Infinitesimal variations; Fundamental equations; Fundamental theorem; 53A07; 53B25;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

This paper deals with the subject of infinitesimal variations of Euclidean submanifolds with arbitrary dimension and codimension. The main goal is to establish a Fundamental theorem for these geometric objects. Similar to the theory of isometric immersions in Euclidean space, we prove that a system of three equations for a certain pair of tensors are the integrability conditions for the differential equation that determines the infinitesimal variations. In addition, we give some rigidity results when the submanifold is intrinsically a Riemannian product of manifolds.

引用

页码：573 / 589

页数：16

共 10 条

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[7]

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