Geodesic
Duality of singularities for flat surfaces in Euclidean space
Journal of Singularities, Tome 21 (2020), pp. 132-148

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In this paper, we shall discuss the duality of singularities for a class of flat surfaces in Euclidean space. After introducing the definition of the conjugate of a tangent developable, we show that, if a tangent developable admits a swallowtail, its conjugate has a cuspidal cross cap. Similarly, we prove that the conjugate of a tangent developable having cuspidal S^+_1 singularities has cuspidal butterflies, and that cuspidal beaks have self-duality. We also show that cuspidal edges do not possess such a property, by exhibiting an example of a tangent developable with cuspidal edges whose conjugate has 5/2-cuspidal edges. Finally, we prove that conjugates of complete flat fronts with embedded ends cannot be complete flat fronts.
DOI : 10.5427/jsing.2020.21h
Classification : 53C42, 57R45. 
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     author = {Atsufumi Honda},
     title = {Duality of singularities for flat surfaces in {Euclidean} space},
     journal = {Journal of Singularities},
     pages = {132--148},
     publisher = {mathdoc},
     volume = {21},
     year = {2020},
     doi = {10.5427/jsing.2020.21h},
     url = {http://geodesic.mathdoc.fr/articles/10.5427/jsing.2020.21h/}
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Atsufumi Honda. Duality of singularities for flat surfaces in Euclidean space. Journal of Singularities, Tome 21 (2020), pp. 132-148. doi: 10.5427/jsing.2020.21h

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