Geodesic
Duality on generalized cuspidal edges preserving singular set images and first fundamental forms
Journal of Singularities, Tome 22 (2020), pp. 59-91

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In the second, fourth and fifth authors' previous work, a duality on generic real analytic cuspidal edges in the Euclidean 3-space 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 R^3, including cuspidal cross caps, and 5/2-cuspidal edges. Moreover, we give several new geometric insights on this duality.
DOI : 10.5427/jsing.2020.22e
Classification : 57R45, 53A05 
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     title = {Duality on generalized cuspidal edges preserving singular set images and first fundamental forms},
     journal = {Journal of Singularities},
     pages = {59--91},
     publisher = {mathdoc},
     volume = {22},
     year = {2020},
     doi = {10.5427/jsing.2020.22e},
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Atsufumi Honda; Kosuke Naokawa; Kentaro Saji; Masaaki Umehara,; Kotaro Yamada. Duality on generalized cuspidal edges preserving singular set images and first fundamental forms. Journal of Singularities, Tome 22 (2020), pp. 59-91. doi: 10.5427/jsing.2020.22e

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