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