2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/147598In this paper we study critial isometric and minimal isometric embeddings of classes of Riemannian metrics which we call {\it quasi-$k$-curved metrics}. Quasi-$k$-curved metrics generalize the metrics of space forms. We construct explicit examples and prove results about existence and rigidity.21 pages, AMSTeX. Significantly changed version of paper originally Titled "On minimal isometric embeddings"Differential Geometrytext