TY - JOUR
T1 - Sur la détermination d'une surface dans ℝ3 à partir de ses deux formes fondamentales
AU - Ciarlet, Philippe G.
AU - Larsonneur, François
PY - 2000/12/1
Y1 - 2000/12/1
N2 - 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.
AB - 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.
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U2 - 10.1016/s0764-4442(00)01728-6
DO - 10.1016/s0764-4442(00)01728-6
M3 - Isn't the information, if a journal is professional or not an attribute of the journal itself and not the article in it? This is to fullfill RGC category.
SN - 0249-6291
VL - 331
SP - 893
EP - 897
JO - Comptes Rendus de l'Academie des Sciences - Series I: Mathematics
JF - Comptes Rendus de l'Academie des Sciences - Series I: Mathematics
IS - 11
ER -