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B-field transformations of Poisson groupoids
B-field transformations Poisson groupoids Symplectic Geometry
2011/9/13
Abstract: In this work we study B-field transformations of multiplicative Poisson bivectors on a Lie groupoid G. We are concerned with B-fields given by multiplicative closed 2-forms on G. We view Poi...
The geometry of embedded pseudo-Riemannian surfaces in terms of Poisson brackets
pseudo-Riemannian manifolds embedded surfaces Poisson brackets
2011/8/25
Abstract: Arnlind, Hoppe and Huisken showed how to express the Gauss and mean curvature of a surface embedded in a Riemannian manifold in terms of Poisson brackets of the embedding coordinates. We gen...
We study the Schr\"odinger-Poisson system on the unit sphere $\SS^2$ of $\RR^3$, modeling the quantum transport of charged particles confined on a sphere by an external potential. Our first results c...
A result of [2] extends the Marsden-Ratiu reduction theorem [4] in Poisson geometry, and is proven by means of graded geometry. In this note we provide the background material about graded geometry ne...
Connections in Poisson Geometry I: Holonomy and Invariants
Connections Poisson Geometry I Holonomy Invariants
2010/11/1
We discuss contravariant connections on Poisson manifolds. For vector bundles, the corresponding operational notion of a contravariant derivative had been introduced by Izu Vaisman. We show that thes...