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Normal developable surfaces of surfaces along curves

Part of: Differential topology

Published online by Cambridge University Press:  06 January 2017

Satoshi Hananoi  and
Shyuichi Izumiya
Satoshi Hananoi
Affiliation:
Fudooka High School, 1-7-45 Fudooka, Kazo, Saitama 347-8513, Japan (noi.87noi@gmail.com)
Shyuichi Izumiya
Affiliation:
Department of Mathematics, Hokkaido University, Sapporo 060-0810, Japan (izumiya@math.sci.hokudai.ac.jp)
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Extract

We consider a developable surface normal to a surface along a curve on the surface. We call it a normal developable surface along the curve on the surface. We investigate the uniqueness and the singularities of such developable surfaces. We discover two new invariants of curves on a surface that characterize these singularities.

Keywords

normal developable surfacescurves on surfacesDarboux frames

MSC classification

Secondary: 57R45: Singularities of differentiable mappings
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 147 , Issue 1 , February 2017 , pp. 177 - 203
Copyright
Copyright © Royal Society of Edinburgh 2017 

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