2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/169996We classify the smooth projective symmetric G-varieties with Picard number one (and G semisimple). Moreover we prove a criterion for the smoothness of the simple (normal) symmetric varieties whose closed orbit is complete. In particular we prove that, given a such variety X which is not exceptional, then X is smooth if and only if an appropriate toric variety contained in X is smooth.23 pages; some minor errors corrected, final version. To appear on "International Journal of Mathematics"Algebraic GeometryRepresentation Theory14M17 (Primary), 14J45, 14L30 (Secondary)text