East Asian mathematical journal

  • 제26권1호
  • /
  • Pages.75-79
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  • 2010
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  • 1226-6973(pISSN)
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  • 2287-2833(eISSN)
영남수학회 (The Youngnam Mathematical Society)
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YANG-MILLS CONNECTIONS ON A COMPACT CONNECTED SEMISIMPLE LIE GROUP

  • Park, Joon-Sik (DEPARTMENT OF MATHEMATICS PUSAN UNIVERSITY OF FOREIGN STUDIES)
  • 투고 : 2009.09.27
  • 심사 : 2010.01.12
  • 발행 : 2010.01.31
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초록

Let G be a compact connected semisimple Lie group, g the Lie algebra of G, g the canonical metric (the biinvariant Riemannian metric which is induced from the Killing form of g), and $\nabla$ be the Levi-Civita connection for the metric g. Then, we get the fact that the Levi-Civita connection $\nabla$ in the tangent bundle TG over (G, g) is a Yang-Mills connection.

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참고문헌

  1. S. Dragomir, T. Ichiyama and H. Urakawa, Yang-Mills theory and conjugate connections, Differential Geom. Appl. 18 (2003), 229-238. https://doi.org/10.1016/S0926-2245(02)00149-3
  2. S. Helgason, Differential Geometry, Lie Groups and Symmetric Spaces, Academic Press, New York, 1978.
  3. S. Kobayashi and K. Nomizu, Foundation of Differential Geometry, Vol. I, Wiley-Interscience, New York, 1963.
  4. K. Nomizu, Invariant ane connections on homogeneous spaces, Amer. J. Math. 76(1954), 33-65. https://doi.org/10.2307/2372398
  5. J. -S. Park, The conjugate connection of a Yang-Mills connection, Kyushu J. Math. 62(2008), 217-220. https://doi.org/10.2206/kyushujm.62.217
  6. J. -S. Park, Yang-Mills connections with Weyl structure, Proc. Japan Acad. 84(A)(2008), 129-132.
  7. Walter A. Poor, Differential Geometric Structures, McGraw-Hill, Inc., 1981.
  8. H. Urakawa, Calculus of Variations and Harmonic Maps, Transl. Math. Monographs,Vol. 99, Amer. Math. Soc., Providence, RI, 1993.