## 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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