On the recovery of a surface with prescribed first and second fundamental forms. (Q1408915)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: On the recovery of a surface with prescribed first and second fundamental forms. |
scientific article; zbMATH DE number 1985990
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the recovery of a surface with prescribed first and second fundamental forms. |
scientific article; zbMATH DE number 1985990 |
Statements
On the recovery of a surface with prescribed first and second fundamental forms. (English)
0 references
25 September 2003
0 references
The paper proves Bonnet's theorem as a corollary of the known theorem which states that if the Riemann-Christoffel tensor associated with a field of positive definite symmetric matrices of order three vanishes in a connected and simply connected open set in \(\mathbb{R}^3\), then this field is the metric tensor field of an open set that can be isometrically imbedded in \(\mathbb{R}^3\) uniquely up to rigid motions.
0 references
Bonnet's theorem
0 references
Riemann-Christoffel tensor
0 references
field of positive definite symmetric matrices
0 references
