Infinitesimal rigidity of Euclidean submanifolds

M. Dajczer; L. L. Rodriguez

Annales de l'institut Fourier (1990)

  • Volume: 40, Issue: 4, page 939-949
  • ISSN: 0373-0956

Abstract

top
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.

How to cite

top

Dajczer, M., and Rodriguez, L. L.. "Infinitesimal rigidity of Euclidean submanifolds." Annales de l'institut Fourier 40.4 (1990): 939-949. <http://eudml.org/doc/74906>.

@article{Dajczer1990,
abstract = {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.},
author = {Dajczer, M., Rodriguez, L. L.},
journal = {Annales de l'institut Fourier},
keywords = {infinitesimally rigid; isometric rigidity},
language = {eng},
number = {4},
pages = {939-949},
publisher = {Association des Annales de l'Institut Fourier},
title = {Infinitesimal rigidity of Euclidean submanifolds},
url = {http://eudml.org/doc/74906},
volume = {40},
year = {1990},
}

TY - JOUR
AU - Dajczer, M.
AU - Rodriguez, L. L.
TI - Infinitesimal rigidity of Euclidean submanifolds
JO - Annales de l'institut Fourier
PY - 1990
PB - Association des Annales de l'Institut Fourier
VL - 40
IS - 4
SP - 939
EP - 949
AB - 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.
LA - eng
KW - infinitesimally rigid; isometric rigidity
UR - http://eudml.org/doc/74906
ER -

References

top
  1. [A] C. B. ALLENDOERFER, Rigidity for spaces of class greater than one, Amer. J. Math., 61 (1939), 633-644. Zbl0021.15803MR1,28gJFM65.0802.01
  2. [CD] M. do CARMO and M. DAJCZER, Conformal rigidity, Amer. J. of Math., 109 (1987), 963-985. Zbl0631.53043MR89e:53016
  3. [DG] M. DAJCZER and D. GROMOLL, Real Kaehler submanifolds and uniqueness of the Gauss map, J. Diff. Geometry, 22 (1985), 13-28. Zbl0587.53051MR87g:53088b
  4. [DR1] M. DAJCZER and L. RODRIGUEZ, Rigidity of real Kaehler submanifolds, Duke Math. J., 53 (1986), 211-220. Zbl0599.53005MR87g:53089
  5. [DR2] M. DAJCZER and L. RODRIGUEZ, Hypersurfaces which make a constant angle, in "Differential Geometry", Longman Sc. & Tech., Harlow, 1990. Zbl0723.53004
  6. [GR] R. A. GOLDSTEIN and P.J. RYAN, Infinitesimal rigidity of submanifolds, J. Diff. Geometry, 10 (1975), 49-60. Zbl0302.53029MR51 #1675
  7. [S] R. SACKSTEDER, On hypersurfaces with no negative sectional curvature, Amer. J. Math., 82 (1960), 609-630. Zbl0194.22701MR22 #7087
  8. [Y] K. YANO, Infinitesimal variations of submanifolds, Kodai Math. J., 1 (1978), 30-44. Zbl0388.53017MR58 #7504

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.