2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/132486We give an optimal upper bound for the first eigenvalue of the untwisted Dirac operator on a compact symmetric space G/H with rk G-rk H\le 1 with respect to arbitrary Riemannian metrics. We also prove a rigidity statement.LaTeX, 11 pages. V2: Rigidity statement added, minor changes. To appearDifferential Geometry53C27; 53C35; 58J50text