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http://dx.doi.org/10.14403/jcms.2011.24.3.10

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)
Publication Information
Journal of the Chungcheong Mathematical Society / v.24, no.3, 2011 , pp. 503-515 More about this Journal
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
Weyl(Einstein-Weyl) structure; projectively flat connection; Yang-Mills connection;
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