Open Access
2016 Isometric deformations of cuspidal edges
Kosuke Naokawa, Masaaki Umehara, Kotaro Yamada
Tohoku Math. J. (2) 68(1): 73-90 (2016). DOI: 10.2748/tmj/1458248863


Along cuspidal edge singularities on a given surface in Euclidean 3-space $\boldsymbol{R}^3$, which can be parametrized by a regular space curve $\hat\gamma(t)$, a unit normal vector field $\nu$ is well-defined as a smooth vector field of the surface. A cuspidal edge singular point is called generic if the osculating plane of $\hat\gamma(t)$ is not orthogonal to $\nu$. This genericity is equivalent to the condition that its limiting normal curvature $\kappa_\nu$ takes a non-zero value. In this paper, we show that a given generic (real analytic) cuspidal edge $f$ can be isometrically deformed preserving $\kappa_\nu$ into a cuspidal edge whose singular set lies in a plane. Such a limiting cuspidal edge is uniquely determined from the initial germ of the cuspidal edge.


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Kosuke Naokawa. Masaaki Umehara. Kotaro Yamada. "Isometric deformations of cuspidal edges." Tohoku Math. J. (2) 68 (1) 73 - 90, 2016.


Published: 2016
First available in Project Euclid: 17 March 2016

zbMATH: 1350.57031
MathSciNet: MR3476137
Digital Object Identifier: 10.2748/tmj/1458248863

Primary: 57R45
Secondary: 53A05

Keywords: cuspidal edge , isometric deformation

Rights: Copyright © 2016 Tohoku University

Vol.68 • No. 1 • 2016
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