The theory of graph-like Legendrian unfoldings and its applications

Journal of Singularities
volume 12 (2015), 53-79

Received 15 April 2014. Received in revised form 29 October 2014.

DOI: 10.5427/jsing.2015.12d

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Abstract:

This is mainly a survey article on the recent development of the theory of graph-like Legendrian unfoldings and its applications. The notion of big Legendrian submanifolds was introduced by Zakalyukin for describing the wave front propagations. Graph-like Legendrian unfoldings belong to a special class of big Legendrian submanifolds. Although this is a survey article, some new original results and the corrected proofs of some results are given.

Keywords:

Wave front propagations, Big wave fronts, graph-like Legendrian unfoldings, Caustics

Mathematical Subject Classification:

Primary 58K05,57R45,32S05 ; Secondary 58K25, 58K60

Author(s) information:

Shyuichi Izumiya
Department of Mathematics
Hokkaido University
Sapporo 060-0810, Japan
email: izumiya@math.sci.hokudai.ac.jp