2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/141112We study a pointwise inequality for submanifolds in real space forms involving the scalar curvature, the normal scalar curvature and the mean curvature. We translate it into an algebraic problem, allowing us to prove a slightly weaker version of it. We also prove the conjecture for certain types of submanifolds of $\mathbb C^n$.to appear in the Proceedings of the International Congress on Pure and Applied Differential Geometry PADGE2007Differential Geometry53B25text