Invariant Metrics with Nonnegative Curvature on SO(4)

Abstract

We derive a curvature-variation formula for a path of left-invariant metrics on a compact Lie group, beginning at a bi-invariant metric. We prove rigidity theorems for paths which remain nonnegatively curved, and we make progress towards a classification of the left-invariant metrics with nonnegative curvature on SO(4).

References in corpus (1)

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