2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/229557We classify the self-similar solutions to a class of Weingarten curvature flow of connected compact convex hypersurfaces, isometrically immersed into space forms with non-positive curvature, and obtain a new characterization of a sphere in a Euclidean space $\R^{n+1}$.12 pages, Latex v2 is a largely extended new versionDifferential Geometry53C24; 53C44text