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Addendum:
Singularities of flat fronts in hyperbolic space
Masatoshi Kokubu, Wayne Rossman, Kentaro Saji, Masaaki Umehara and Kotaro Yamada |
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Vol. 294 (2018), No. 2, 505–509
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Correction to Pacific Journal of Mathematics 221:2 (2005) 303–351 |
Abstract |
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This is an addendum to the authors’ previous paper in which criteria for cuspidal edges and swallowtails on surfaces are given by applying the so-called Zakalyukin’s lemma. The original statement in Zakalyukin’s paper assumed the properness of the mappings. However, the lemma in the appendix of our paper did not assume properness. Recently, we noticed that the proof given in the appendix was implicitly relying on properness. In this addendum, we prove that mappings satisfying the criteria of cuspidal edges and swallowtails have properness. Consequently, the criteria are clarified. |
Keywords
wave front, cuspidal edge, swallowtail
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Mathematical Subject Classification 2010
Primary: 53C42, 57R45
Secondary: 53A05, 53A99
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Milestones
Received: 16 November 2016
Accepted: 17 October 2017
Published: 20 February 2018
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Authors |
| Masatoshi Kokubu | |
| Department of Mathematics, School of
Engineering Tokyo Denki University Tokyo Japan |
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| Wayne Rossman | |
| Department of Mathematics, Faculty
of Science Kobe University Kobe Japan |
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| Kentaro Saji | |
| Department of Mathematics, Graduate
School of Science Kobe University Kobe Japan |
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| Masaaki Umehara | |
| Department of Mathematical and
Computing Sciences Tokyo Institute of Technology Tokyo Japan |
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| Kotaro Yamada | |
| Department of Mathematics Tokyo Institute of Technology Tokyo Japan |
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