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On instability of Yang-Mills connections. (English) Zbl 0634.53022
In this article, extending previous results on the standard sphere \(S^ n\) (n\(\geq 5)\) by Jim Simons, the authors exhibit examples of manifolds over which any nonflat Yang-Mills field is unstable. Their examples cover the Cayley plane, \(E_ 6/F_ 4\) and some isoparametric minimal hypersurfaces of spheres.
On the way they compute very thoroughly the second variation of the Yang- Mills functional for manifolds isometrically immersed in Euclidean spaces, in particular minimal submanifolds of spheres. Out of their technical tools is the maximum eigenvalue of the curvature operator which they tabulate for all irreducible compact symmetric spaces.
Reviewer: J.P.Bourguignon

MSC:
53C05 Connections (general theory)
58E99 Variational problems in infinite-dimensional spaces
53C42 Differential geometry of immersions (minimal, prescribed curvature, tight, etc.)
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