Dual Killing-Yano symmetry and multipole moments in electromagnetism and mechanics of continua

In this work we introduce the Killing-Yano symmetry on the phase space and we investigate the symplectic structure on the space of Killing-Yano tensors. We perform the detailed analyze of the ndimensional flat space and the Riemaniann manifolds with constant scalar curvature. We investigate the form of some multipole tensors, which arise in the expansion of a system of charges and currents, in terms of second-order Killing-Yano tensors in the phase space of classical mechanics. We find some relations between these tensors and the generators of dynamical symmetries like the angular momentum, the mass-inertia tensor, the conformal operator and the momentum conjugate Runge-Lenz vector. 1 Permanent address:Institute of Space Sciences, P.O.BOX, MG-23, R 76900, MagureleBucharest, Romania, E-mail: [email protected],[email protected] 3 Permanent address:Department for Theoretical Physics, National Institute for Nuclear Physics, POB MG-6, Bucharest-Măgurele, Romania