AFFINE YANG-MILLS CONNECTIONS ON NORMAL HOMOGENEOUS SPACES

• Journal title : Honam Mathematical Journal
• Volume 33, Issue 4,  2011, pp.557-573
• Publisher : The Honam Mathematical Society
• DOI : 10.5831/HMJ.2011.33.4.557
Title & Authors
AFFINE YANG-MILLS CONNECTIONS ON NORMAL HOMOGENEOUS SPACES
Park, Joon-Sik;

Abstract
Let G be a compact and connected semisimple Lie group, H a closed subgroup, g (resp. h) the Lie algebra of G (resp. H), B the Killing form of g, g the normal metric on the homogeneous space G/H which is induced by -B. Let D be an invarint connection with Weyl structure (D, g, $\small{{\omega}}$) in the tangent bundle over the normal homogeneous Riemannian manifold (G/H, g) which is projectively flat. Then, the affine connection D on (G/H, g) is a Yang-Mills connection if and only if D is the Levi-Civita connection on (G/H, g).
Keywords
Yang-Mills connection;Weyl structure;invariant connection;normal homogeneous Riemannian manifold;
Language
English
Cited by
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