Kyushu Journal of Mathematics
Online ISSN : 1883-2032
Print ISSN : 1340-6116
ISSN-L : 1340-6116
PROJECTIVELY FLAT YANG-MILLS CONNECTIONS
Joon-Sik PARK
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2009 Volume 64 Issue 1 Pages 49-58

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Abstract
Let (M, g) be an n-dimensional (n ≥ 3) closed (compact and connected) Riemannian manifold. We obtain a necessary and sufficient condition for a projectively flat connection D with a Weyl structure (D, g, ω) in the tangent bundle TM over (M, g) to be a Yang-Mills connection. Moreover, we get the fact that the condition dω = 0 is a necessary and sufficient condition for the Ricci tensor RicD of a connection D with Weyl structure (D, g, ω) in the bundle TM over (M, g) to be symmetric, and then we get a necessary and sufficient condition for a projectively flat Einstein-Weyl connection D in the bundle TM over (M, g) to be a Yang-Mills connection.
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© Faculty of Mathematics, Kyushu University
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