Obstructions to Positive Curvature on Homogeneous Bundles

Details Obstructions to Positive Curvature on Homogeneous Bundles Obstructions to Positive Curvature on Homogeneous Bundles

2005-08-21

arxiv.org/abs/math/0508394v1

Mathematics

Metric Geometry

Scientific paper

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.

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