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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Nonrigidity of a class of two dimensional surfaces with positive curvature and planar points


Author: A. Meziani
Journal: Proc. Amer. Math. Soc. 141 (2013), 2137-2143
MSC (2010): Primary 53A05; Secondary 30G20, 35F05
Published electronically: January 25, 2013
MathSciNet review: 3034439
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Abstract: Existence of nontrivial infinitesimal bendings is established for an orientable surface with boundary $ S\subset \mathbb{R}^3$ that has positive curvature except at finitely many planar points and such that $ H_1(S)=0$. As an application, we show that any neighborhood of such a surface $ S$ (for the $ C^k$ topology) contains isometric surfaces that are noncongruent.


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Additional Information

A. Meziani
Affiliation: Department of Mathematics, Florida International University, Miami, Florida 33199
Email: meziani@fiu.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-2013-11488-7
PII: S 0002-9939(2013)11488-7
Keywords: Infinitesimal bending, surface, positive curvature, asymptotic direction
Received by editor(s): December 10, 2009
Received by editor(s) in revised form: October 4, 2011
Published electronically: January 25, 2013
Communicated by: Sergei K. Suslov
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.