2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/58561A method of constructing a class of bihamiltonian structures is presented. Elements of this class are generalizations of the so-called bihamiltonian structures of general position on odd-dimensional manifolds. The method consists in a simultaneous reduction of both the real and imaginary parts of a complex symplectic form. Necessary and sufficient conditions of getting a bihamiltonian structure from the mentioned class are obtained. The second part of the paper is devoted to a series of examples of such a reduction related to semisimple Lie algebras.41p. The revised version presents the main result in a more general form. The paper is essentially reconstructedDifferential Geometry58F07, 53A60text