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On the flat ridges of submanifolds of codimension 2 in Rn

Published online by Cambridge University Press:  12 July 2007

M. C. Romero-Fuster  and
E. Sanabria-Codesal
M. C. Romero-Fuster
Affiliation:
Departamento de Geometria i Topologia, Universitat de Valncia, Spain (romeromc@post.uv.es)
E. Sanabria-Codesal
Affiliation:
Departamento de Matemtica Aplicada, Universidad Politcnica de Valncia, Spain (esanabri@mat.upv.es)
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Abstract

We introduce the concept of flat ridges for submanifolds of codimension 2 from the viewpoint of their contact with hyperplanes. We characterize them geometrically, studying some of their properties. In particular, we see that the highest-order flat ridges coincide with the flattenings of the asymptotic lines and from this we obtain some lower bounds for their numbers under appropriate conditions.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 132 , Issue 4 , August 2002 , pp. 975 - 984
Copyright
Copyright © Royal Society of Edinburgh 2002

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