2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/36214In this paper the symmetries of the dual manifold were investigated. We found the conditions when the manifold and its dual admit the same Killing vectors and Killing-Yano tensors. In the case of an Einstein's metric $g_{μν}$ the corresponding equations for its dual were found. The examples of Kerr-Newman geometry and the separable coordinates in 1+1 dimensions were analyzed in details.10 pages,LATEX, content revisedGeneral Relativity and Quantum Cosmologytext