Conditions for Nonnegative Curvature on Vector Bundles and Sphere Bundles

Kristopher Tapp

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Conditions for Nonnegative Curvature on Vector Bundles and Sphere Bundles

Kristopher Tapp

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Abstract

This paper addresses Cheeger and Gromoll's question of which vector bundles admit a complete metric of nonnegative curvature, and relates their question to the issue of which sphere bundles admit a metric of positive curvature. We show that any vector bundle which admits a metric of nonnegative curvature must admit a connection, a tensor, and a metric on the base space which together satisfy a certain differential inequality. On the other hand, a slight sharpening of this condition is sufficient for the associated sphere bundle to admit a metric of positive curvature. Our results sharpen and generalize Walschap and Strake's conditions under which a vector bundle admits a connection metric of nonnegative curvature.

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BibTeX RIS

Kristopher Tapp. 2002-10-10. Conditions for Nonnegative Curvature on Vector Bundles and Sphere Bundles. https://arxiv.org/abs/math/0210160

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