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YANG-MILLS CONNECTIONS ON A COMPACT CONNECTED SEMISIMPLE LIE GROUP

Joon-Sik Park
영남수학회 (Youngnam Mathematical Society)|2010.01|East Asian Mathematical Journal|제26권 제1호|pp. 75-79

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참고문헌

키워드

Yang-Mills connectioncompact connected semisimple Lie groupcanonical metric
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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 ∇ be the Levi-Civita connection for the metric g. Then, we get the fact that the Levi-Civita connection ∇ in the tangent bundle TG over (G,g) is a Yang-Mills connection.

Abstract

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 ∇ be the Levi-Civita connection for the metric g. Then, we get the fact that the Levi-Civita connection ∇ in the tangent bundle TG over (G,g) is a Yang-Mills connection.

참고문헌 (8)

  1. S. Dragomir, "Yang-Mills theory and conjugate connections", Dierential Geom. Appl., 18, pp.229~238 (2003)
  2. S. Helgason, "Dierential Geometry, Lie Groups and Symmetric Spaces" (1978), Academic Press
  3. S. Kobayashi, "Foundation of Derential Geometry, Vol. I" (1963), Wiley-Interscience
  4. K. Nomizu, "Invariant ane connections on homogeneous spaces", Amer. J. Math, 76, pp.33~65 (1954)
  5. J. -S. Park, "The conjugate connection of a Yang-Mills connection", Kyushu J. Math, 62, pp.217~220 (2008)
  6. J. -S. Park, "Yang-Mills connections with Weyl structure", Proc. Japan Acad, 통권 : 84, pp.129~132 (2008)
  7. Walter A. Poor, "Dierential Geometric Structures" (1981), McGraw-Hill, Inc.
  8. H. Urakawa, "Calculus of Variations and Harmonic Maps, Vol. 99" (1993), Providence

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