Abstract mechanical connection and Abelian reconstruction for almost Kähler manifolds.
Pekarsky, Sergey, Marsden, Jerrold E. (2001)
Journal of Applied Mathematics
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Pekarsky, Sergey, Marsden, Jerrold E. (2001)
Journal of Applied Mathematics
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Toshihiro Iwai (1987)
Annales de l'I.H.P. Physique théorique
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Božidar Jovanović (2012)
Publications de l'Institut Mathématique
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Frank Loose (1997)
Annales de l'institut Fourier
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A Liouville form on a symplectic manifold is by definition a potential of the symplectic form . Its center is given by . A normal form for certain Liouville forms in a neighborhood of its center is given.
Janyška, Josef
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In this nice paper the author proves that all natural symplectic forms on the tangent bundle of a pseudo-Riemannian manifold are pull-backs of the canonical symplectic form on the cotangent bundle with respect to some diffeomorphisms which are naturally induced by the metric.
Viktor Ginzburg, Richard Montgomery (2000)
Banach Center Publications
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A geometric quantization of a Kähler manifold, viewed as a symplectic manifold, depends on the complex structure compatible with the symplectic form. The quantizations form a vector bundle over the space of such complex structures. Having a canonical quantization would amount to finding a natural (projectively) flat connection on this vector bundle. We prove that for a broad class of manifolds, including symplectic homogeneous spaces (e.g., the sphere), such connection does not exist....