Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
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WEYL STRUCTURES ON COMPACT CONNECTED LIE GROUPS

  • Park, Joon-Sik (Department of Mathematics Pusan University of Foreign Studies) ;
  • Pyo, Yong-Soo (Department of Applied Mathematics Pukyong National University) ;
  • Shin, Young-Lim (Department of Applied Mathematics Pukyong National University)
  • Received : 2011.06.01
  • Accepted : 2011.08.13
  • Published : 2011.09.30
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Abstract

Let G be a compact connected semisimple Lie group, B the Killing form of the algebra g of G, and g the invariant metric induced by B. Then, we obtain a necessary and sufficient condition for a left invariant linear connection D with a Weyl structure ($D,\;g,\;{\omega}$) on (G, g) to be projectively flat (resp. Einstein-Weyl). And, we also get that if a left invariant linear connection D with a Weyl structure ($D,\;g,\;{\omega}$) on (G, g) which has symmetric Ricci tensor $Ric^D$ is projectively flat, then the connection D is Einstein-Weyl; but the converse is not true. Moreover, we show that if a left invariant connection D with Weyl structure ($D,\;g,\;{\omega}$) on (G, g) is projectively flat (resp. Einstein-Weyl), then D is a Yang-Mills connection.

Keywords

Acknowledgement

Supported by : Pukyong National University

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