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Manifolds with almost nonnegative curvature operator and principal bundles

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Abstract

We study closed manifolds with almost nonnegative curvature operator (ANCO) and derive necessary and/or sufficient conditions for the total spaces of principal bundles over (A)NCO manifolds to admit ANCO connection metrics. In particular, we provide first examples of closed simply connected ANCO manifolds which do not admit metrics with nonnegative curvature operator.

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Authors and Affiliations

  1. Fakultät für Mathematik, Karlsruher Institut für Technologie (KIT), Kaiserstraße 89-93, 76133 , Karlsruhe, Germany

    Martin Herrmann, Dennis Sebastian & Wilderich Tuschmann

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  1. Martin Herrmann
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  2. Dennis Sebastian
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  3. Wilderich Tuschmann
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Correspondence to Wilderich Tuschmann.

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Herrmann, M., Sebastian, D. & Tuschmann, W. Manifolds with almost nonnegative curvature operator and principal bundles. Ann Glob Anal Geom 44, 391–399 (2013). https://doi.org/10.1007/s10455-013-9372-2

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  • DOI: https://doi.org/10.1007/s10455-013-9372-2

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