Induction of Hamiltonian Poisson actions

We propose a Poisson-Lie analog of the symplectic induction procedure, using an appropriate Poisson generalization of the reduction of symplectic manifolds with symmetry. Having as basic tools the equivariant momentum maps of Poisson actions, the double group of a Poisson-Lie group and the reduction of Poisson manifolds with symmetry, we show how one can induce a Poisson action admitting an equivariant momentum map. We prove that, under certain conditions, the dressing orbits of a Poisson-Lie group can be obtained by Poisson induction from the dressing orbits of a Poisson-Lie subgroup.Comment: 17 pages, Plain TeX file, to appear in Diff. Geom. App

A construction of symplectic connections through reduction

We give an elementary construction of symplectic connections through reduction. This provides an elegant description of a class of symmetric spaces and gives examples of symplectic connections with Ricci type curvature, which are not locally symmetric; the existence of such symplectic connections was unknown.Comment: 16 pages, Plain TeX fil

Semidirect products and the Pukanszky condition

We study the general geometrical structure of the coadjoint orbits of a semidirect product formed by a Lie group and a representation of this group on a vector space. The use of symplectic induction methods gives new insight into the structure of these orbits. In fact, each coadjoint orbit of such a group is obtained by symplectic induction on some coadjoint orbit of a "smaller" Lie group. We study also a special class of polarizations related to a semidirect product and the validity of Pukanszky's condition for these polarizations. Some examples of physical interest are discussed using the previous methods.Comment: 33 pages, including special macros and fonts (JGPpaper.tex is the source TeX file), to appear in J. Geom. Phys., also available via anonymous ftp or via gopher gopher://cpt.univ-mrs.fr

The validation service of the hydrological SAF geostationary and polar satellite precipitation products

Abstract. The development phase (DP) of the EUMETSAT Satellite Application Facility for Support to Operational Hydrology and Water Management (H-SAF) led to the design and implementation of several precipitation products, after 5 yr (2005–2010) of activity. Presently, five precipitation estimation algorithms based on data from passive microwave and infrared sensors, on board geostationary and sun-synchronous platforms, function in operational mode at the H-SAF hosting institute to provide near real-time precipitation products at different spatial and temporal resolutions. In order to evaluate the precipitation product accuracy, a validation activity has been established since the beginning of the project. A Precipitation Product Validation Group (PPVG) works in parallel with the development of the estimation algorithms with two aims: to provide the algorithm developers with indications to refine algorithms and products, and to evaluate the error structure to be associated with the operational products. In this paper, the framework of the PPVG is presented: (a) the characteristics of the ground reference data available to H-SAF (i.e. radar and rain gauge networks), (b) the agreed upon validation strategy settled among the eight European countries participating in the PPVG, and (c) the steps of the validation procedures. The quality of the reference data is discussed, and the efforts for its improvement are outlined, with special emphasis on the definition of a ground radar quality map and on the implementation of a suitable rain gauge interpolation algorithm. The work done during the H-SAF development phase has led the PPVG to converge into a common validation procedure among the members, taking advantage of the experience acquired by each one of them in the validation of H-SAF products. The methodology is presented here, indicating the main steps of the validation procedure (ground data quality control, spatial interpolation, up-scaling of radar data vs. satellite grid, statistical score evaluation, case study analysis). Finally, an overview of the results is presented, focusing on the monthly statistical indicators, referred to the satellite product performances over different seasons and areas

Superization of Homogeneous Spin Manifolds and Geometry of Homogeneous Supermanifolds

Let M_0=G_0/H be a (pseudo)-Riemannian homogeneous spin manifold, with reductive decomposition g_0=h+m and let S(M_0) be the spin bundle defined by the spin representation Ad:H->\GL_R(S) of the stabilizer H. This article studies the superizations of M_0, i.e. its extensions to a homogeneous supermanifold M=G/H whose sheaf of superfunctions is isomorphic to Lambda(S^*(M_0)). Here G is the Lie supergroup associated with a certain extension of the Lie algebra of symmetry g_0 to an algebra of supersymmetry g=g_0+g_1=g_0+S via the Kostant-Koszul construction. Each algebra of supersymmetry naturally determines a flat connection nabla^{S} in the spin bundle S(M_0). Killing vectors together with generalized Killing spinors (i.e. nabla^{S}-parallel spinors) are interpreted as the values of appropriate geometric symmetries of M, namely even and odd Killing fields. An explicit formula for the Killing representation of the algebra of supersymmetry is obtained, generalizing some results of Koszul. The generalized spin connection nabla^{S} defines a superconnection on M, via the super-version of a theorem of Wang.Comment: 50 page