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

Jack Huizenga·Kristopher Tapp
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Abstract

We 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.

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Jack Huizenga, Kristopher Tapp. 2007-02-09. Invariant metrics with nonnegative curvature on SO(4) and other Lie groups. https://arxiv.org/abs/math/0702241

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