Isometric deformations of compact Euclidean submanifolds in codimension $2$
Marcos Dajczer and Detlef Gromoll
Source: Duke Math. J. Volume 79, Number 3
(1995), 605-618.
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.dmj/1077285351
Mathematical Reviews number (MathSciNet): MR1355178
Zentralblatt MATH identifier: 0857.53005
Digital Object Identifier: doi:10.1215/S0012-7094-95-07915-0
References
[Ca] É. Cartan, La déformation des hypersurfaces dans l'espace euclidean réel à n dimensions, Bull. Soc. Math. France 44 (1916), 65–99.
Zentralblatt MATH: 46.1129.01
[CD] M. do Carmo and M. Dajczer, A rigidity theorem for higher codimensions, Math. Ann. 274 (1986), no. 4, 577–583.
Mathematical Reviews (MathSciNet): MR87h:53067
Zentralblatt MATH: 0579.53006
Digital Object Identifier: doi:10.1007/BF01458592
[Da1] M. Dajczer, et al., Submanifolds and isometric immersions, Mathematics Lecture Series, vol. 13, Publish or Perish Inc., Houston, TX, 1990.
Mathematical Reviews (MathSciNet): MR92i:53049
Zentralblatt MATH: 0705.53003
[Da2] M. Dajczer, A characterization of complex hypersurfaces in $\mathbfC^m$, Proc. Amer. Math. Soc. 105 (1989), no. 2, 425–428.
Mathematical Reviews (MathSciNet): MR89f:53090
Zentralblatt MATH: 0661.53014
Digital Object Identifier: doi:10.2307/2046960
JSTOR: links.jstor.org
[DG1] M. Dajczer and D. Gromoll, Gauss parametrizations and rigidity aspects of submanifolds, J. Differential Geom. 22 (1985), no. 1, 1–12.
Mathematical Reviews (MathSciNet): MR87g:53088a
Zentralblatt MATH: 0588.53007
Project Euclid: euclid.jdg/1214439717
[DG2] M. Dajczer and D. Gromoll, Real Kaehler submanifolds and uniqueness of the Gauss map, J. Differential Geom. 22 (1985), no. 1, 13–28.
Mathematical Reviews (MathSciNet): MR87g:53088b
Zentralblatt MATH: 0587.53051
Project Euclid: euclid.jdg/1214439718
[DG3] M. Dajczer and D. Gromoll, Rigidity of complete euclidean hypersurfaces, J. Differential Geom. 31 (1990), no. 2, 401–416.
Mathematical Reviews (MathSciNet): MR91d:53083
Zentralblatt MATH: 0667.53003
Project Euclid: euclid.jdg/1214444321
[DT] M. Dajczer and R. Tojeiro, On submanifolds of two manifolds, Math. Z. 214 (1993), no. 3, 405–413.
Mathematical Reviews (MathSciNet): MR95b:53075
Zentralblatt MATH: 0799.53071
Digital Object Identifier: doi:10.1007/BF02572413
[Fe] D. Ferus, On the completeness of nullity foliations, Michigan Math. J. 18 (1971), 61–64.
Mathematical Reviews (MathSciNet): MR43:5454
Zentralblatt MATH: 0193.22003
Digital Object Identifier: doi:10.1307/mmj/1029000589
Project Euclid: euclid.mmj/1029000589
[Gr] M. Gromov, Partial Differential Relations, Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)], vol. 9, Springer-Verlag, Berlin, 1986.
Mathematical Reviews (MathSciNet): MR90a:58201
Zentralblatt MATH: 0651.53001
[Hi] M. Hirsch, Immersions of manifolds, Trans. Amer. Math. Soc. 93 (1959), 242–276.
Mathematical Reviews (MathSciNet): MR22:9980
Zentralblatt MATH: 0113.17202
Digital Object Identifier: doi:10.2307/1993453
JSTOR: links.jstor.org
[KN] S. Kobayashi and K. Nomizu, Foundations of differential geometry. Vol. II, Interscience Tracts in Pure and Applied Mathematics, No. 15 Vol. II, Interscience Publishers John Wiley & Sons, Inc., New York-London-Sydney, 1969.
Mathematical Reviews (MathSciNet): MR38:6501
Zentralblatt MATH: 0175.48504
[Sa] R. Sacksteder, The rigidity of hypersurfaces, J. Math. Mech. 11 (1962), 929–939.
Mathematical Reviews (MathSciNet): MR26:1833
Zentralblatt MATH: 0108.34702
[Sb] U. Sbrana, Sulle varietá ad $n-1$ dimensione deformabili nello spazio euclideo ad $n$ dimensione, Rend. Circ. Mat. Palermo 27 (1909), 1–45.
Zentralblatt MATH: 40.0716.02
[Sp] M. Spivak, A Comprehensive Introduction to Differential Geometry, Publish or Perish, Houston, 1979.
Duke Mathematical Journal
