Energy gap for Yang-Mills connections, I: Four-dimensional closed Riemannian manifolds

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• 作者：Paul M.N. Feehan¹ ; ^{feehan@math.rutgers.edu" class="auth_mail" title="E-mail the corresponding author} ; ^{feehan@math.ias.edu" class="auth_mail" title="E-mail the corresponding author}
• 关键词：primary ; 58E15 ; 57R57 ; secondary ; 37D15 ; 58D27 ; 70S15 ; 81T13
• 刊名：Advances in Mathematics
• 出版年：2016
• 出版时间：25 June 2016
• 年：2016
• 卷：296
• 期：Complete
• 页码：55-84
• 全文大小：611 K

文摘

We extend an L²$L^2$ energy gap result due to Min-Oo [28, Theorem 2] and Parker [30, Proposition 2.2] for Yang–Mills connections on principal G-bundles, P, over closed, connected, four-dimensional, oriented, smooth manifolds, X, from the case of positive Riemannian metrics to the more general case of good Riemannian metrics, including metrics that are generic and where the topologies of P and X obey certain mild conditions and the compact Lie group, G  , is SU(2)$\mathrm{SU}(2)$ or SO(3)$\mathrm{SO}(3)$.