2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/115423We derive a curvature-variation formula for a path of left-invariant metrics on a compact Lie group, beginning at a bi-invariant metric. We prove rigidity theorems for paths which remain nonnegatively curved, and we make progress towards a classification of the left-invariant metrics with nonnegative curvature on SO(4).Differential GeometryMetric Geometry53Ctext