Nonnegatively curved 5-manifolds with non-abelian symmetry
Differential Geometry
2012-12-21 v1
Abstract
We classify compact simply-connected 5-dimensional manifolds which admit a metric of nonnegative curvature with a connected non-abelian group acting by isometries. We show that they are diffeomorphic to either S^5, S^3 x S^2, the nontrivial S^3-bundle over S^2 or the Wu-manifold, SU(3)/SO(3). This result is a consequence of our equivariant classification of all SO(3) and SU(2)-actions on compact simply-connected 5-manifolds. In the case of positive curvature we obtain a partial classification.
Keywords
Cite
@article{arxiv.1212.5022,
title = {Nonnegatively curved 5-manifolds with non-abelian symmetry},
author = {Fabio Simas},
journal= {arXiv preprint arXiv:1212.5022},
year = {2012}
}
Comments
22 pages