ISOMETRIC DEFORMATIONS OF CUSPIDAL EDGES

• Naokawa Kosuke

  Department of Mathematics, Faculty of Science, Kobe University

• Umehara Masaaki

  Department of Mathematical and Computing Sciences, Tokyo Institute of Technology

• Yamada Kotaro

  Department of Mathematics, Tokyo Institute of Technology

Abstract

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.

Journal

• Tohoku Mathematical Journal, Second Series

  Tohoku Mathematical Journal, Second Series 68 (1), 73-90, 2016-03-30

  Mathematical Institute, Tohoku University

Keywords

• Cuspidal edge
• isometric deformation

Details

• CRID: 1390008299688843776
• NII Article ID: 130008106069
• DOI: 10.2748/tmj/1458248863
• ISSN: 2186585X
• ISSN: 00408735
• Text Lang: en
• Data Source:
  • JaLC
  • Crossref
  • CiNii Articles
  • KAKEN
• Abstract License Flag: Disallowed