Resumen: We construct invariant generalized Gauduchon metrics on the product of two complex nilmanifolds that do not necessarily admit this kind of metrics. In particular, we prove that the product of a locally conformal Kähler nilmanifold and a balanced nilmanifold admits a generalized Gauduchon metric. In complex dimension 4, generalized Gauduchon nilmanifolds with (the highest possible) nilpotency step are given, as well as 3-step and 4-step examples for which the center of their underlying Lie algebras does not contain any non-trivial J-invariant ideal. These examples show strong differences between the SKT and the generalized Gauduchon geometries of nilmanifolds. Idioma: Inglés DOI: 10.1016/j.difgeo.2017.03.016 Año: 2017 Publicado en: DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS 54, Part A (2017), 151-164 [15 p.] ISSN: 0926-2245 Factor impacto JCR: 0.76 (2017) Categ. JCR: MATHEMATICS rank: 131 / 309 = 0.424 (2017) - Q2 - T2 Categ. JCR: MATHEMATICS, APPLIED rank: 170 / 252 = 0.675 (2017) - Q3 - T3 Factor impacto SCIMAGO: 0.791 - Analysis (Q2) - Geometry and Topology (Q2) - Computational Theory and Mathematics (Q2)