Canonical relations defined by intersecting hypersurfaces in a symplectic manifold
type: Item
instance of: scholarly article
title: Canonical relations defined by intersecting hypersurfaces in a symplectic manifold
zbMATH Open document ID: 0577.53030
DOI: 10.1007/BF01456130
author: Humio Suzuki
published in: Mathematische Annalen
publication date: 1985-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/163982
review text: The main result: Suppose that (F,G) (resp. \((\tilde F,\tilde G))\) is a non-singular pair of intersecting conic hypersurfaces in a conic symplectic manifold \((M,m_ 0)\) (resp. \((\tilde M,\tilde m_ 0))\) and \(\Gamma =\Gamma_{F,G}=\{(k,\ell)\in M_ F\times M_ G\), \(k\cap \ell \neq \emptyset \}\) is the homogeneous canonical relation. Then two pairs of hypersurfaces (F,G) and \((\tilde F,\tilde G)\) are locally equivalent at \((m_ 0,\tilde m_ 0)\) if and only if the corresponding homogeneous canonical relations \(\Gamma\) at \((\pi_{F^{m_ 0}},\pi_{G^{m_ 0}})\) and \({\tilde \Gamma}\) at \((\pi_{\tilde F^{\tilde m_ 0}},\pi_{\tilde G^{\tilde m_ 0}})\) are locally equivalent.
Mathematics Subject Classification ID: 53C15
zbMATH DE Number: 3923604
zbMATH Keywords: intersecting conic hypersurfaces
zbMATH Keywords: symplectic manifold
zbMATH Keywords: canonical relation
reviewed by: Constantin Udrişte
MaRDI profile type: Publication
cites work: Fourier integral operators. I
cites work: Equivalence of glancing hyper-surfaces
cites work: Equivalence of glancing hypersurfaces. II
cites work: Q4160040
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description: scientific article; zbMATH DE number 3923604