Stability and isolation phenomena for Yang-Mills fields |
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Authors: | Jean-Pierre Bourguignon H Blaine Lawson Jr |
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Institution: | (1) Ecole Polytechnique, Centre de Mathématiques, F-91128 Palaiseau Cedex, France;(2) Institut des Hautes Études Scientifiques, F-91140 Bures-sur-Yvette, France;(3) Department of Mathematics, State University of New York, 11790 Stony Brook, N.Y., USA |
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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.Laboratoire Associé au C.N.R.S. No. 169Research partially supported by Volkswagen Grant and NSF Grant MCS-77-23579 |
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