For any admissible real analytic cuspidal edge along a knot, uncountably many non-congruent cuspidal edges share the same first fundamental form.
Brander, Spherical surfaces, Experimental Mathematics 25 (2016), 257–272
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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.