2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/123639We develop techniques for classifying the nonnegatively curved left-invariant metrics on a compact Lie group G. We prove rigidity theorems for general G and a partial classification for G=SO(4). Our approach is to reduce the general question to an infinitesimal version; namely, to classify the directions one can move away from a fixed bi-invariant metric such that curvature variation formulas predict nearby metrics are nonnnegatively curved.22 pagesDifferential GeometryMetric Geometry53Ctext