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Integral representations over isotropic submanifolds and equations of zero curvature. (English) Zbl 0926.53030

The following setting is considered. There is a submanifold \(\Lambda\) of the cotangent bundle \(T^*M\) of a Riemannian manifold \(M\) which is invariant under the Hamiltonian flow and which is isotropic, i.e., the form \(p dq\) is closed on \(\Lambda.\) The authors work with a global integral representation for quasimodes for the quantum Hamiltonian. This leads to certain geometrical objects over an isotropic submanifold.

MSC:

53D05 Symplectic manifolds (general theory)
53C40 Global submanifolds
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