Isometric rigidity in codimension 2
Marcos Dajczer and Pedro Morais
Source: Michigan Math. J. Volume 58, Issue 3
(2009), 759-770.
First Page:
Show
Hide
Full-text: Access denied (no subscription
detected)
We're sorry, but we are unable to provide
you with the full text of this article because we are not able to identify
you as a subscriber.
If you have a personal subscription to
this journal, then please login. If you are already logged in, then you
may need to update your profile to register your subscription. Read more about accessing full-text
Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.mmj/1260475699
Digital Object Identifier: doi:10.1307/mmj/1260475699
Zentralblatt MATH identifier: 05665443
Mathematical Reviews number (MathSciNet): MR2595563
References
C. Allendoerfer, Rigidity for spaces of class greater than one, Amer. J. Math. 61 (1939), 633--644.
Mathematical Reviews (MathSciNet): MR170
Digital Object Identifier: doi:10.2307/2371317
JSTOR: links.jstor.org
J. L. Barbosa, M. Dajczer, and L. Jorge, Minimal ruled submanifolds in spaces of constant curvature, Indiana Univ. Math. J. 33 (1984), 531--547.
Mathematical Reviews (MathSciNet): MR749313
Zentralblatt MATH: 0544.53044
Digital Object Identifier: doi:10.1512/iumj.1984.33.33028
R. Beez, Zur Theorie des Krümmungsmasses von Mannigfaltigkeiten höhere Ordnung, Zeit. für Math. und Physik 21 (1876), 373--401.
L. Bianchi, Sulle varietà a tre dimensioni deformabili entro lo spazio euclideo a quattro dimensioni, Memorie di Matematica e di Fisica della Società Italiana delle Scienze, ser. III, t. XIII (1905), 261--323.
M. do Carmo and M. Dajczer, Conformal rigidity, Amer. J. Math. 109 (1987), 963--985.
Mathematical Reviews (MathSciNet): MR910359
Zentralblatt MATH: 0631.53043
Digital Object Identifier: doi:10.2307/2374496
JSTOR: links.jstor.org
E. Cartan, La déformation des hypersurfaces dans l'espace euclidien réel a $n$ dimensions, Bull. Soc. Math. France 44 (1916), 65--99.
Mathematical Reviews (MathSciNet): MR1504750
M. Dajczer, M. Antonucci, G. Oliveira, P. Lima-Filho, and R. Tojeiro, Submanifolds and isometric immersions, Math. Lecture Ser., 13, Publish or Perish, Houston, TX, 1990.
Mathematical Reviews (MathSciNet): MR1075013
Zentralblatt MATH: 0705.53003
M. Dajczer and L. Florit, Genuine rigidity of Euclidean submanifolds in codimension two, Geom. Dedicata 106 (2004), 195--210.
Mathematical Reviews (MathSciNet): MR2079843
Zentralblatt MATH: 1076.53022
Digital Object Identifier: doi:10.1023/B:GEOM.0000033846.63094.46
------, Genuine deformations of submanifolds, Comm. Anal. Geom. 5 (2004), 1105--1121.
Mathematical Reviews (MathSciNet): MR2103313
M. Dajczer, L. Florit, and R. Tojeiro, On deformable hypersurfaces in space forms, Ann. Mat. Pura Appl. (4) 147 (1998), 361--390.
Mathematical Reviews (MathSciNet): MR1746935
Zentralblatt MATH: 0956.53043
Digital Object Identifier: doi:10.1007/BF01759378
M. Dajczer and D. Gromoll, Rigidity of complete Euclidean hypersurfaces, J. Differential Geom. 31 (1990), 401--416.
Mathematical Reviews (MathSciNet): MR1037409
Zentralblatt MATH: 0667.53003
Project Euclid: euclid.jdg/1214444321
------, Isometric deformations of compact Euclidean submanifolds in codimension 2, Duke Math. J. 79 (1995), 605--618.
Mathematical Reviews (MathSciNet): MR1355178
Zentralblatt MATH: 0857.53005
Digital Object Identifier: doi:10.1215/S0012-7094-95-07915-0
Project Euclid: euclid.dmj/1077285351
W. Killing, Die nicht-Euklidischen Raumformen in analytische Behandlung, Teubner, Leipzig, 1885.
J. D. Moore, Submanifolds of constant positive curvature, I, Duke Math. J. 44 (1977), 449--484.
Mathematical Reviews (MathSciNet): MR438256
Zentralblatt MATH: 0361.53050
Digital Object Identifier: doi:10.1215/S0012-7094-77-04421-0
Project Euclid: euclid.dmj/1077312242
V. Sbrana, Sulla varietá ad $n-1$ dimensioni deformabili nello spazio euclideo ad $n$ dimensioni, Rend. Circ. Mat. Palermo 27 (1909), 1--45.
F. Schur, Ueber die Deformation eines dreidimensionalen Raumes in einem ebenen vierdimensionalen Raum, Math. Ann. 28 ( 1886), 343--353.
M. Spivak, A comprehensive introduction to differential geometry, vol. IV, Publish or Perish, Wilmington, DE, 1979.
Mathematical Reviews (MathSciNet): MR532833
Zentralblatt MATH: 0439.53004
The Michigan Mathematical Journal
