Vol. 294, No. 2, 2018

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ISSN: 0030-8730
Addendum: Singularities of flat fronts in hyperbolic space

Masatoshi Kokubu, Wayne Rossman, Kentaro Saji, Masaaki Umehara and Kotaro Yamada

Vol. 294 (2018), No. 2, 505–509

Correction to Pacific Journal of Mathematics 221:2 (2005) 303–351

Abstract

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
Mathematical Subject Classification 2010
Primary: 53C42, 57R45
Secondary: 53A05, 53A99
Milestones
Received: 16 November 2016
Accepted: 17 October 2017
Published: 20 February 2018
Authors
Masatoshi Kokubu
Department of Mathematics, School of Engineering
Tokyo Denki University
Tokyo
Japan
Wayne Rossman
Department of Mathematics, Faculty of Science
Kobe University
Kobe
Japan
Kentaro Saji
Department of Mathematics, Graduate School of Science
Kobe University
Kobe
Japan
Masaaki Umehara
Department of Mathematical and Computing Sciences
Tokyo Institute of Technology
Tokyo
Japan
Kotaro Yamada
Department of Mathematics
Tokyo Institute of Technology
Tokyo
Japan