Yang-Mills connections of cohomogeneity one on SO(n)-bundles over Euclidean spheres

Details Yang-Mills connections of cohomogeneity one on SO(n)-bundles over Euclidean spheres Yang-Mills connections of cohomogeneity one on SO(n)-bundles over Euclidean spheres

2011-07-29

arxiv.org/abs/1107.5952v1

Mathematics

Differential Geometry

27 pages

Scientific paper

We construct Yang-Mills connections on SO(n)-bundles over spheres equipped with the Euclidean metric. We use a cohomogeneity one group action on the bundle to reduce the Yang-Mills-equation to a system of ordinary differential equations. The system is shown to have solutions by variational methods, using ideas from harmonic map theory. Examples include Yang-Mills connections on each of the countably many principal SO(6)-bundles over $S^6$, and countably many Yang-Mills connections on $TS^n$ for $n\in\{5,...,9\}$.

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