and
Laboratoire de Physique Th\'eorique et des Hautes Energies,
CNRS, Unit\'e associ\'ee URA 280,
2 Place Jussieu, 75251 Paris Cedex 05, FRANCE
E-mail: gvalent@cpt.univ-mrs.fr, gal.valent@wanadoo.fr
Higher conserved quantities for the multi-centre metrics
Abstract:
The multi-centre metrics are a family of euclidean solutions of the
empty space Einstein equations with self-dual curvature. We consider the
hamiltonian dynamics generated by the geodesic flow along the U(1) fibers
and obtain several metrics in this class which do exhibit an extra
conserved quantity quadratic in the
momenta. The corresponding systems are shown to be classically integrable.
The relation of these results with some three-dimensional integrable systems
with
potential is given.