Metrics of negative curvature on vector bundles

Anderson, Michael T.

doi:10.1090/S0002-9939-1987-0870801-8

Metrics of negative curvature on vector bundles
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by Michael T. Anderson

Proc. Amer. Math. Soc. 99 (1987), 357-363

DOI: https://doi.org/10.1090/S0002-9939-1987-0870801-8

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Abstract:

It is shown that any vector bundle $E$ over a compact base manifold $M$ admits a complete metric of negative (respectively nonpositive) curvature provided $M$ admits a metric of negative (nonpositive) curvature.

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