2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/104714Having in mind the well known model of Euclidean convex hypersurfaces [4], [5], and the ideas in [1] many authors defined and investigate convex hypersurfaces of a Riemannian manifold. As it was proved by the first author in [7], there follows the interdependence between convexity and Gauss curvature of the hypersurface. In this paper we define $H$-convexity of a Riemannian submanifold of arbitrary codimension, replacing the normal versor of a hypersurface with the mean curvature vector $H$. A characterization, used by B.Y. Chen [2], [3] as the definition of strictly $H$-convexity, it is obtained.8 pages; The paper is now included in the PhD Thesis of Teodor OpreaDifferential GeometryOptimization and Control53C40, 53C45text