Flat surfaces along swallowtails

Shyuichi Izumiya; Kentaro Saji; Keisuke Teramoto

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arXiv · 1709.06133

Flat surfaces along swallowtails

Shyuichi Izumiya·Kentaro Saji·Keisuke Teramoto

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Abstract

We consider developable surfaces along the singular set of a swallowtail which are considered to be flat approximations of the swallowtail. For the study of singularities of such developable surfaces, we introduce the notion of Darboux frames along swallowtails and invariants. As a by-product, we give a new example of a frontal which is locally homeomorphic to a swallowtail.

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Shyuichi Izumiya, Kentaro Saji, Keisuke Teramoto. 2017-09-18. Flat surfaces along swallowtails. https://arxiv.org/abs/1709.06133

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