Sur la détermination d'une surface dans ℝ3 à partir de ses deux formes fondamentales

Research output: Journal Publications and ReviewsRGC 22 - Publication in policy or professional journal

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Original languageFrench
Pages (from-to)893-897
Journal / PublicationComptes Rendus de l'Academie des Sciences - Series I: Mathematics
Volume331
Issue number11
Publication statusPublished - 1 Dec 2000
Externally publishedYes

Abstract

It is known that the knowledge of the first and second fundamental forms satisfying the theorema egregium of Gauss and the Codazzi-Mainardi identities determines a surface in ℝ3, uniquely up to isometries of ℝ3. It is shown here how this theorem can be deduced from the theorem establishing the determination of a three-dimensional manifold in ℝ3 from the knowledge of a metric tensor whose associated Riemann-Christoffel tensor vanishes. © 2000 Académie des sciences/Éditions scientifiques et médicales Elsevier SAS.