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AFFINE YANG-MILLS CONNECTIONS ON NORMAL HOMOGENEOUS SPACES

Park, Joon-Sik

  • Received : 2011.09.28
  • Accepted : 2011.10.18
  • Published : 2011.12.25

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, ${\omega}$) 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

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