Homogeneous Metrics with nonnegative curvature

Details Homogeneous Metrics with nonnegative curvature Homogeneous Metrics with nonnegative curvature

2008-04-23

arxiv.org/abs/0804.3729v2

Mathematics

Differential Geometry

Scientific paper

Given compact Lie groups H\subset G, we study the space of G-invariant metrics on G/H with nonnegative sectional curvature. For an intermediate subgroup K between H and G, we derive conditions under which enlarging the Lie algebra of K maintains nonnegative curvature on G/H. Such an enlarging is possible if (K,H) is a symmetric pair, which yields many new examples of nonnegatively curved homogeneous metrics. We provide other examples of spaces G/H with unexpectedly large families of nonnegatively curved homogeneous metrics.

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