Can I read Bour's Theorem for Helicoidal Surfaces with Singularities on EtoBox?

Bour's Theorem for Helicoidal Surfaces with Singularities by Hattori, Yuki; Honda, Atsufumi; Morimoto, Tatsuya is a scholarly article available to read on EtoBox.

What is Bour's Theorem for Helicoidal Surfaces with Singularities about?

In this paper, generalizing the techniques of Bour's theorem, we prove that every generic cuspidal edge, more generally, generic $n$-type edge, which is invariant under a helicoidal motion in Euclidean $3$-space admits non-trivial isometric deformations. As a corollary, several geometric invariants, such as the limiting normal curvature, the cusp-directional torsion, the higher order cuspidal curvature and the bias, are proved to be extrinsic invariants.

Author

Hattori, Yuki; Honda, Atsufumi; Morimoto, Tatsuya

Published

2023

Language

EN