Techniques for Classifying Nonnegatively Curved Left-invariant Metrics on Compact Lie Groups
نویسنده
چکیده
We provide techniques for studying the nonnegatively curved leftinvariant 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).
منابع مشابه
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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...
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