Abstract
In this article a series of results concerning Yang-Mills fields over the euclidean sphere and other locally homogeneous spaces are proved using differential geometric methods. One of our main results is to prove that any weakly stable Yang-Mills field overS 4 with groupG=SU2, SU3 orU 2 is either self-dual or anti-self-dual. The analogous statement for SO4-bundles is also proved. The other main series of results concerns gap-phenomena for Yang-Mills fields. As a consequence of the non-linearity of the Yang-Mills equations, we can give explicitC 0-neighbourhoods of the minimal Yang-Mills fields which contain no other Yang-Mills fields. In this part of the study the nature of the groupG does not matter, neither is the dimension of the base manifold constrained to be four.
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Communicated by A. Jaffe
Laboratoire Associé au C.N.R.S. No. 169
Research partially supported by Volkswagen Grant and NSF Grant MCS-77-23579
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Bourguignon, JP., Lawson, H.B. Stability and isolation phenomena for Yang-Mills fields. Commun.Math. Phys. 79, 189–230 (1981). https://doi.org/10.1007/BF01942061
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DOI: https://doi.org/10.1007/BF01942061