Canonical relations defined by intersecting hypersurfaces in a symplectic manifold
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.
scientific article; zbMATH DE number 3923604
scientific article