# Obstruction to Positive Curvature on Homogeneous Bundles

```@article{Tapp2005ObstructionTP,
title={Obstruction to Positive Curvature on Homogeneous Bundles},
author={Kristopher Tapp},
journal={Geometriae Dedicata},
year={2005},
volume={119},
pages={105-112}
}```
Examples of almost-positively and quasi-positively curved spaces of the form M = H\((G, h) × F) were discovered recently [J. Differential Geom. 65:273–287, 2003; Invent. Math. 148:117–141, 2002]. Here h is a left-invariant metric on a compact Lie group G, F is a compact Riemannian manifold on which the subgroup \$\$H\subset G\$\$ acts isometrically on the left, and M is the orbit space of the diagonal left action of H on (G, h) × F with the induced Riemannian submersion metric. We prove that no new… Expand

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