Bour's theorem for helicoidal surfaces with singularities

Yuki Hattori; Atsufumi Honda; Tatsuya Morimoto

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arXiv · 2310.16418

Bour's theorem for helicoidal surfaces with singularities

Yuki Hattori·Atsufumi Honda·Tatsuya Morimoto

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Abstract

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.

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Yuki Hattori, Atsufumi Honda, Tatsuya Morimoto. 2023-10-25. Bour's theorem for helicoidal surfaces with singularities. https://arxiv.org/abs/2310.16418

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