Homogeneous Metrics with nonnegative curvature
Differential Geometry
2008-06-24 v2 Metric Geometry
Abstract
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.
Keywords
Cite
@article{arxiv.0804.3729,
title = {Homogeneous Metrics with nonnegative curvature},
author = {Lorenz Schwachhofer and Kristopher Tapp},
journal= {arXiv preprint arXiv:0804.3729},
year = {2008}
}