2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/228050A surface S in R^3 has the central plane oval property (cpo) if (i) S meets at least one affine plane transversally along a strictly convex oval, and (ii) Every such transverse oval on S has central symmetry. We show that a complete, connected C^2 surface with cpo must be either a generalized cylinder, or quadric. Applying this, we deduce that a complete C^2 surface containing a transverse plane oval but no skewloop, must be a cylinder or a quadric.35 pages, 3 figuresDifferential Geometry53A05; 53A15text