A submanifold of the Euclidean space 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.
Une sous-variété de l’espace euclidien 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.
@article{AIF_1990__40_4_939_0, author = {Dajczer, M. and Rodriguez, L. L.}, title = {Infinitesimal rigidity of {Euclidean} submanifolds}, journal = {Annales de l'Institut Fourier}, pages = {939--949}, publisher = {Institut Fourier}, address = {Grenoble}, volume = {40}, number = {4}, year = {1990}, doi = {10.5802/aif.1242}, zbl = {0727.53011}, mrnumber = {92d:53048}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.1242/} }
TY - JOUR AU - Dajczer, M. AU - Rodriguez, L. L. TI - Infinitesimal rigidity of Euclidean submanifolds JO - Annales de l'Institut Fourier PY - 1990 SP - 939 EP - 949 VL - 40 IS - 4 PB - Institut Fourier PP - Grenoble UR - https://aif.centre-mersenne.org/articles/10.5802/aif.1242/ DO - 10.5802/aif.1242 LA - en ID - AIF_1990__40_4_939_0 ER -
%0 Journal Article %A Dajczer, M. %A Rodriguez, L. L. %T Infinitesimal rigidity of Euclidean submanifolds %J Annales de l'Institut Fourier %D 1990 %P 939-949 %V 40 %N 4 %I Institut Fourier %C Grenoble %U https://aif.centre-mersenne.org/articles/10.5802/aif.1242/ %R 10.5802/aif.1242 %G en %F AIF_1990__40_4_939_0
Dajczer, M.; Rodriguez, L. L. Infinitesimal rigidity of Euclidean submanifolds. Annales de l'Institut Fourier, Volume 40 (1990) no. 4, pp. 939-949. doi : 10.5802/aif.1242. https://aif.centre-mersenne.org/articles/10.5802/aif.1242/
[A] Rigidity for spaces of class greater than one, Amer. J. Math., 61 (1939), 633-644. | JFM | MR | Zbl
,[CD] Conformal rigidity, Amer. J. of Math., 109 (1987), 963-985. | MR | Zbl
and ,[DG] Real Kaehler submanifolds and uniqueness of the Gauss map, J. Diff. Geometry, 22 (1985), 13-28. | MR | Zbl
and ,[DR1] Rigidity of real Kaehler submanifolds, Duke Math. J., 53 (1986), 211-220. | MR | Zbl
and ,[DR2] Hypersurfaces which make a constant angle, in "Differential Geometry", Longman Sc. & Tech., Harlow, 1990. | Zbl
and ,[GR] Infinitesimal rigidity of submanifolds, J. Diff. Geometry, 10 (1975), 49-60. | MR | Zbl
and ,[S] On hypersurfaces with no negative sectional curvature, Amer. J. Math., 82 (1960), 609-630. | MR | Zbl
,[Y] Infinitesimal variations of submanifolds, Kodai Math. J., 1 (1978), 30-44. | MR | Zbl
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