2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/126249Let $(M,g)$ be a compact Riemannian manifold on dimension $n \geq 4$ not conformally diffeomorphic to the sphere $S^n$. We prove that a smooth function $f$ on $M$ is a critical function for a metric $\tilde{g}$ conformal to $g$ if and only if there exists $x \in M$ such that $f(x)>0$.Differential Geometry53C21, 46E35, 26D10text