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A counterexample to a conjecture on flat bilinear forms

Author(s): Marcos Dajczer; Luis A. Florit
Journal: Proc. Amer. Math. Soc. 132 (2004), 3703-3704.
MSC (2000): Primary 53B25
Posted: July 22, 2004
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Abstract | References | Similar articles | Additional information

Abstract: We provide a counterexample to a conjecture on the dimension of the nullity of a flat symmetric bilinear form.

References:

[1]
M. do Carmo and M. Dajczer, Conformal Rigidity, Amer. J. Math. 109 (1987), 963-985. MR 0910359 (89e:53016)

[2]
E. Cartan, La déformation des hypersurfaces dans l'espace conforme réel a $n\geq 5$ dimensions. Bull. Soc. Math. France 45 (1917), 57-121.

[3]
M. Dajczer and L. A. Florit, Compositions of isometric immersions in higher codimension, Manuscripta Math. 105 (2001), 507-517; Erratum, Manuscripta Math. 110 (2003), 135. MR 1858501 (2002m:53096); MR 1951804 (2003m:53101)

[4]
M. Dajczer and R. Tojeiro, A rigidity theorem for conformal immersions, Indiana Univ. Math. J. 46 (1997), 491-504. MR 1481600 (98j:53072)

[5]
J. D. Moore, Submanifolds of constant positive curvature I, Duke Math. J. 44 (1977), 449-484. MR 0438256 (55:11174)

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Additional Information:

Marcos Dajczer
Affiliation: IMPA, Estrada Dona Castorina, 110, 22460-320, Rio de Janeiro, Brazil
Email: marcos@impa.br

Luis A. Florit
Affiliation: IMPA, Estrada Dona Castorina, 110, 22460-320, Rio de Janeiro, Brazil
Email: luis@impa.br

DOI: 10.1090/S0002-9939-04-07636-1
PII: S 0002-9939(04)07636-1
Keywords: Symmetric flat bilinear form, nullity
Received by editor(s): July 1, 2001
Posted: July 22, 2004
Communicated by: Wolfgang Ziller
Copyright of article: Copyright 2004, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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