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We develop techniques for classifying the nonnegatively curved left-invariantmetrics on a compact Lie group G. We prove rigidity theorems for general G anda partial classification for G=SO(4). Our approach is to reduce the generalquestion to an infinitesimal version; namely, to classify the directions onecan move away from a fixed bi-invariant metric such that curvature variationformulas predict nearby metrics are nonnnegatively curved.

Invariant metrics with nonnegative curvature on SO(4) and other Lie groups