The Lie bialgebroid of a Poisson-Nijenhuis manifold

Abstract. We describe a new class of Lie bialgebroids associated with Poisson-Nijenhuis structures. Résumé. Nous étudions une nouvelle classe de bigébröıdes de Lie, associés aux structures de Poisson-Nijenhuis. Introduction. Nijenhuis operators have been introduced in the theory of integrable sys-tems in the work of Magri, Gelfand and Dorfman (see the book [4]), and, under the name of hereditary operators, in that of Fuchssteiner and Fokas. Poisson-Nijenhuis structures were defined by Magri and Morosi in 1984 [15] in their study of completely integrable systems. There is a compatibility condition between the Poisson structure and the Nijenhuis struc