3 years ago

On the geometry of folded cuspidal edges

Raúl Oset Sinha, Kentaro Saji

Abstract

We study the geometry of cuspidal \(S_k\) singularities in \({\mathbb {R}}^3\) obtained by folding generically a cuspidal edge. In particular we study the geometry of the cuspidal cross-cap M, i.e. the cuspidal \(S_0\) singularity. We study geometrical invariants associated to M and show that they determine it up to order 5. We then study the flat geometry (contact with planes) of a generic cuspidal cross-cap by classifying submersions which preserve it and relate the singularities of the resulting height functions with the geometric invariants.

Open access
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