2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/129786The paper provides a different proof of the result of Brendle-Schoen on the differential sphere theorem. It is shown directly that the invariant cone of curvature operators with positive (or non-negative) complex sectional curvature is preserved by the Ricci flow. This implies, by a result of Böhm-Wilking, that the normalized Ricci flow deforms such a metric to a metric of constant positive curvature. Using earlier work of Yau and Zheng it can be shown that a metric with strictly (pointwise) 1/4-pinched sectional curvature has positive complex sectional curvature. This gives a direct proof of Brendle-Schoen's recent differential sphere theorem, bypassing any discussion of positive isotropic curvature.Differential Geometry53C21, 58J35text