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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Invariant connections and Yang-Mills solutions


Author: Mitsuhiro Itoh
Journal: Trans. Amer. Math. Soc. 267 (1981), 229-236
MSC: Primary 53C05; Secondary 53C99, 55R10, 57S15, 81E10
MathSciNet review: 621984
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Abstract: A condition on the self-duality and the stability of Yang-Mills solutions are discussed. The canonical invariant $ G$-connections on $ {S^4}$ and $ {P_2}({\mathbf{C}})$ are considered as Yang-Mills solutions. The non-self-duality of the connections requires the injectivity of the isotropy homomorphisms. We construct examples of non-self-dual connections on $ G$-vector bundles ($ G$ is a compact simple group). Under a certain property of the isotropy homomorphism, these canonical connections are not weakly stable.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1981-0621984-5
PII: S 0002-9947(1981)0621984-5
Keywords: Yang-Mills solution, canonical connection, self-duality, stability
Article copyright: © Copyright 1981 American Mathematical Society