Manifolds with almost nonnegative curvature operator and principal bundles
- First Online:
- Cite this article as:
- Herrmann, M., Sebastian, D. & Tuschmann, W. Ann Glob Anal Geom (2013) 44: 391. doi:10.1007/s10455-013-9372-2
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.