Techniques for classifying nonnegatively curved left-invariant metrics on compact Lie groups

Details Techniques for classifying nonnegatively curved left-invariant metrics on compact Lie groups Techniques for classifying nonnegatively curved left-invariant metrics on compact Lie groups

2006-08-14

arxiv.org/abs/math/0608362v1

Mathematics

Differential Geometry

13 pages

Scientific paper

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).

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