Infinitesimal rigidity of Euclidean submanifolds
Annales de l'Institut Fourier, Tome 40 (1990) no. 4, pp. 939-949.

Une sous-variété Mn de l’espace euclidien Rn est dite infinitésimalement rigide si toute déformation différentiable isométrique au premier ordre est triviale. Nous montrons ici que certaines conditions locales ou globales bien connues pour entraîner la rigidité isométrique entraînent aussi la rigidité infinitésimale.

A submanifold Mn of the Euclidean space Rn is said to be infinitesimally rigid if any smooth variation which is isometric to first order is trivial. The main purpose of this paper is to show that local or global conditions which are well known to imply isometric rigidity also imply infinitesimal rigidity.

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     author = {Dajczer, M. and Rodriguez, L. L.},
     title = {Infinitesimal rigidity of {Euclidean} submanifolds},
     journal = {Annales de l'Institut Fourier},
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Dajczer, M.; Rodriguez, L. L. Infinitesimal rigidity of Euclidean submanifolds. Annales de l'Institut Fourier, Tome 40 (1990) no. 4, pp. 939-949. doi : 10.5802/aif.1242. https://www.numdam.org/articles/10.5802/aif.1242/

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