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

Une sous-variété M n de l’espace euclidien R n 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 M n of the Euclidean space R n 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.

@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, Tome 40 (1990) no. 4, pp. 939-949. doi : 10.5802/aif.1242. https://aif.centre-mersenne.org/articles/10.5802/aif.1242/

[A] C. B. Allendoerfer, Rigidity for spaces of class greater than one, Amer. J. Math., 61 (1939), 633-644. | JFM | MR | Zbl

[CD] M. Do Carmo and M. Dajczer, Conformal rigidity, Amer. J. of Math., 109 (1987), 963-985. | MR | Zbl

[DG] M. Dajczer and D. Gromoll, Real Kaehler submanifolds and uniqueness of the Gauss map, J. Diff. Geometry, 22 (1985), 13-28. | MR | Zbl

[DR1] M. Dajczer and L. Rodriguez, Rigidity of real Kaehler submanifolds, Duke Math. J., 53 (1986), 211-220. | MR | Zbl

[DR2] M. Dajczer and L. Rodriguez, Hypersurfaces which make a constant angle, in "Differential Geometry", Longman Sc. & Tech., Harlow, 1990. | Zbl

[GR] R. A. Goldstein and P.J. Ryan, Infinitesimal rigidity of submanifolds, J. Diff. Geometry, 10 (1975), 49-60. | MR | Zbl

[S] R. Sacksteder, On hypersurfaces with no negative sectional curvature, Amer. J. Math., 82 (1960), 609-630. | MR | Zbl

[Y] K. Yano, Infinitesimal variations of submanifolds, Kodai Math. J., 1 (1978), 30-44. | MR | Zbl

Cité par Sources :