Annals of Global Analysis and Geometry

, Volume 44, Issue 4, pp 391–399 | Cite as

Manifolds with almost nonnegative curvature operator and principal bundles

  • Martin Herrmann
  • Dennis Sebastian
  • Wilderich Tuschmann


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.


Curvature operator Nonnegative curvature Principal bundle 

Mathematics Subject Classification (1991)

Primary 53C23 57C21 Secondary 57R55 


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Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  • Martin Herrmann
    • 1
  • Dennis Sebastian
    • 1
  • Wilderich Tuschmann
    • 1
  1. 1.Fakultät für MathematikKarlsruher Institut für Technologie (KIT)KarlsruheGermany

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