2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/56577We show that, in finite dimensions, the only monotone metrics for which the (+1) and (-1) affine connections are mutually dual are constant multiples of Bogoliubov-Kubo-Mori metricPublished version, includes comparison with related uniquines results and the explicit extension of monotone metrics from density operators to denormalized faithful. weightsMathematical PhysicsDifferential Geometry82C10, 53Z05text