Displaying similar documents to “On the integrability of orthogonal distributions in Poisson manifolds.”

Aspects of Geometric Quantization Theory in Poisson Geometry

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.

Singular Poisson reduction of cotangent bundles.

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.

Symplectic connections with parallel Ricci tensor

Michel Cahen, Simone Gutt, John Rawnsley (2000)

Banach Center Publications

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A variational principle introduced to select some symplectic connections leads to field equations which, in the case of the Levi Civita connection of Kähler manifolds, are equivalent to the condition that the Ricci tensor is parallel. This condition, which is stronger than the field equations, is studied in a purely symplectic framework.

Some Remarks on Dirac Structures and Poisson Reductions

Zhang-Ju Liu (2000)

Banach Center Publications

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Dirac structures are characterized in terms of their characteristic pairs defined in this note and then Poisson reductions are discussed from the point of view of Dirac structures.

Canonical symplectic structures on the r-th order tangent bundle of a symplectic manifold.

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.