Obstructions to Positive Curvature on Homogeneous Bundles
Metric Geometry
2007-05-23 v1 Differential Geometry
Abstract
Examples of almost-positively and quasi-positively curved spaces of the form M=H((G,h)xF) were discovered recently. Here, h is a left-invariant metric on a compact Lie group G, F is a compact Riemannian manifold on which the subgroup H of G acts isometrically on the left, and M is the orbit space of the diagonal left action of H on (G,h)xF with the induced Riemannian submersion metric. We prove that no new examples of strictly positive sectional curvature exist in this class of metrics. This result generalizes the case F={point} proven by Geroch.
Cite
@article{arxiv.math/0508394,
title = {Obstructions to Positive Curvature on Homogeneous Bundles},
author = {Kristopher Tapp},
journal= {arXiv preprint arXiv:math/0508394},
year = {2007}
}