  We provide techniques for studying the nonnegatively curved left-invariant
metrics on a compact Lie group. For "straight" paths of left-invariant metrics
starting at bi-invariant metrics and ending at nonnegatively curved metrics, we
deduce a nonnegativity property of the initial derivative of curvature. We
apply this result to obtain a partial classification of the nonnegatively
curved left-invariant metrics on SO(4).
