2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/169153We establish extremality of Riemannian metrics g with non-negative curvature operator on symmetric spaces M=G/K of compact type with rk(G)-rk(K)\le 1. Let g' be another metric with scalar curvature k', such that g'\ge g on 2-vectors. We show that k'\ge k everywhere on M implies k'=k. Under an additional condition on the Ricci curvature of g, k'\ge k even implies g'=g. We also study area-non-increasing spin maps onto such Riemannian manifolds.13 pages, LaTeX, uses amsartDifferential Geometry53c21 (primary), 53c35, 58j20 (secondary)text