Note on duality on polarized symplectic manifolds
We use some of our earlier results of [Trans. Am. Math. Soc. 252, 163-195 (1979; Zbl 0423.14008)] to derive a general duality theorem for the cohomologies of foliated structures on a manifold. The result is applied to the special case of symplectic manifold M on which the foliation is given by a complex polarization F in the sense of geometric quantization. We obtain, for example, a rigorous proof of the fact that for a smooth function f on M whose Hamiltonian vector field leaves F invariant, the spectrum of the corresponding prequantization operator v(f) coincides with the spectrum of its transpose, under the above duality. This latter result was obtained by D. J. Simms.
cohomologies of foliated structures on a manifold
scientific article; zbMATH DE number 3971817
scientific article