On families of Lagrangian submanifolds

Shyuichi Izumiya and Masatomo Takahashi

Journal of Singularities
volume 21 (2020), 167-186

Received: 26 March 2018. Received in revised form: 17 May 2019.

DOI: 10.5427/jsing.2020.21j

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Abstract:

Lagrangian equivalence among Lagrangian submanifolds and S.P^+-Legendrian equivalence among graph-like Legendrian unfoldings are equivalent. We investigate r-parameter families of Lagrangian submanifolds and r-parameter families of graph-like Legendrian unfoldings. Then we show that r-parameter families of Lagrangian equivalence and r-parameter families of S.P^+-Legendrian equivalence are equivalent. As an application, we give a generic classification of bifurcations of Lagrangian submanifold germs for lower dimensions.

2010 Mathematical Subject Classification:

57R45, 53D12, 37J20, 58K40

Key words and phrases:

Lagrangian singularity, Legendrian singularity, graph-like Legendrian unfolding, bifurcation

Author(s) information:

Shyuichi Izumiya	Masatomo Takahashi
Department of Mathematics	Muroran Institute of Technology
Hokkaido University	Muroran 050-8585, Japan
Sapporo 060-0810, Japan
email: izumiya@math.sci.hokudai.ac.jp	email: masatomo@mmm.muroran-it.ac.jp