Invariant metrics with nonnegative curvature on SO(4) and other Lie groups
Differential Geometry
2007-05-23 v1 Metric Geometry
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.
Keywords
Cite
@article{arxiv.math/0702241,
title = {Invariant metrics with nonnegative curvature on SO(4) and other Lie groups},
author = {Jack Huizenga and Kristopher Tapp},
journal= {arXiv preprint arXiv:math/0702241},
year = {2007}
}
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22 pages