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Duality on generalized cuspidal edges preserving singular set images and first fundamental forms
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abstract
In the second, fourth and fifth authors' previous work, a duality on generic real analytic cuspidal edges in the Euclidean 3-space $\boldsymbol R^3$ preserving their singular set images and first fundamental forms, was given. Here, we call this an `isometric duality'. When the singular set image has no symmetries and does not lie in a plane, the dual cuspidal edge is not congruent to the original one. In this paper, we show that this duality extends to generalized cuspidal edges in $\boldsymbol R^3$, including cuspidal cross caps, and $5/2$-cuspidal edges. Moreover, we give several new geometric insights on this duality.
Forward citations
Cited by 2 Pith papers
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Isometric deformations of mixed type surfaces in Lorentz-Minkowski space
Real analytic generic mixed type surfaces in Lorentz-Minkowski space admit nontrivial local isometric deformations at lightlike points, and the lightlike normal curvature is extrinsic.
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Cuspidal edges with the same first fundamental forms along a knot
For any admissible real analytic cuspidal edge along a knot, uncountably many non-congruent cuspidal edges share the same first fundamental form.
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