Geometric structures on spaces of weighted submanifolds.
Lee, Brian (2009)
SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]
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Lee, Brian (2009)
SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]
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Vaisman, Izu (1985)
International Journal of Mathematics and Mathematical Sciences
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Jan Kurek, Wlodzimierz M. Mikulski (2006)
Extracta Mathematicae
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We describe all canonical 2-forms Λ(ω) on the r-th order tangent bundle TM = J (;M) of a symplectic manifold (M, ω). As a corollary we deduce that all canonical symplectic structures Λ(ω) on TM over a symplectic manifold (M, ω) are of the form Λ(ω) = Σ αω for all real numbers α with α ≠ 0, where ω is the (k)-lift (in the sense of A. Morimoto) of ω to TM.
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.
Simon Hochgerner, Armin Rainer (2006)
Revista Matemática Complutense
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We consider the Poisson reduced space (T* Q)/K, where the action of the compact Lie group K on the configuration manifold Q is of single orbit type and is cotangent lifted to T* Q. Realizing (T* Q)/K as a Weinstein space we determine the induced Poisson structure and its symplectic leaves. We thus extend the Weinstein construction for principal fiber bundles to the case of surjective Riemannian submersions Q → Q/K which are of single orbit type.
Cornelia Vizman (2011)
Archivum Mathematicum
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Differential forms on the Fréchet manifold of smooth functions on a compact -dimensional manifold can be obtained in a natural way from pairs of differential forms on and by the hat pairing. Special cases are the transgression map (hat pairing with a constant function) and the bar map (hat pairing with a volume form). We develop a hat calculus similar to the tilda calculus for non-linear Grassmannians [6].
Vaisman, I. (2001)
Rendiconti del Seminario Matematico
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Fish, Dan, Preston, Serge (2010)
Balkan Journal of Geometry and its Applications (BJGA)
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Izu Vaisman (2000)
Banach Center Publications
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This is a survey exposition of the results of [14] on the relationship between the geometric quantization of a Poisson manifold, of its symplectic leaves and its symplectic realizations, and of the results of [13] on a certain kind of super-geometric quantization. A general formulation of the geometric quantization problem is given at the beginning.