Browse > Article
http://dx.doi.org/10.5831/HMJ.2010.32.4.651

YANG-MILLS CONNECTIONS ON CLOSED LIE GROUPS  

Pyo, Yong-Soo (Department of Applied Mathematics Pukyong National University)
Shin, Young-Lim (Department of Applied Mathematics Pukyong National University)
Park, Joon-Sik (Department of Mathematics Pusan University of Foreign Studies)
Publication Information
Honam Mathematical Journal / v.32, no.4, 2010 , pp. 651-661 More about this Journal
Abstract
In this paper, we obtain a necessary and sufficient condition for a left invariant connection in the tangent bundle over a closed Lie group with a left invariant metric to be a Yang-Mills connection. Moreover, we have a necessary and sufficient condition for a left invariant connection with a torsion-free Weyl structure in the tangent bundle over SU(2) with a left invariant Riemannian metric g to be a Yang-Mills connection.
Keywords
Yang-Mills connection; conjugate connection; torsion-free Weyl structure;
Citations & Related Records
Times Cited By KSCI : 1  (Citation Analysis)
연도 인용수 순위
1 H. Pedersen, Y. S. Poon and A. Swann, Einstein-Weyl deformations and sub-manifolds, Internat. J. Math. 7 (1996), 705-719.   DOI   ScienceOn
2 Walter A. Poor, Differential Geometric Structures, McGraw-Hill, Inc. 1981.
3 Y.-S. Pyo, H. W. Kim and J.-S. Park, On Ricci curvatures of left invariant metrics on SU(2), Bull. Kor. Math, Soc. 46 (2009), 255-261.   DOI   ScienceOn
4 K. Sugahara, The sectional curvature and the diameter estimate for the left invariant metrics on SU(2,C) and SO(3.R), Math. Japonica 26 (1981), 153-159.
5 S. Helgeson, Differential Geometry, Lie Groups and Symmetric Spaces, Academic Press, New York, 1978.
6 M. Itob, Compact Einstein-Weyl manifolds and the associated constant, Osaka J. Math. 35 (1998), 567-578.
7 S. Kobayashi and K. Nomizu, Foundations of Differential Geometry, Vol. 1, Wiley-Interscience, New York, 1963.
8 Y. Matsushima, Differentiable Manifolds, Marcel Dekker, Inc, 1972.
9 I. Mogi and M. Itob, Differential Geometry and Gauge Theory (in Japanese), Kyoritsu Publ., 1986.
10 J. Milnor, Curvatures of left invariant metrics on Lie group, Adv. Math. 21 (1976), 293-329.   DOI
11 K. Nomizu, Invariant affine connections on homogeneous spaces, Amer. J. Math. 76 (1954), 33-65.   DOI   ScienceOn
12 K. Normizu and T. Sasaki, Affine Differential Geometry - Geometry of Affine Immersions, Cambridge Univ. Press, 1994.
13 J.-S. Park, Yang-Mills connections in orthonormal frame bundles over SU(2), Tsukuba J. Math. 18 (1994), 203-206.   DOI
14 J.-S. Park, Critical homogeneous metrics on the Heisenberg manifold, Inter. Inform. Sci. 11 (2005), 31-34.
15 J.-S. Park, The conjugate connection of a Yang-Mills connection, Kyushu J. Math 62 (2008), 217-220.   DOI   ScienceOn
16 J.-S. Park, Yang-Mills connection with Weyl structure, Proc. Japan Academy, 84, Ser. A (2008), 129-132.   DOI
17 J.-S. Park, Invariant Yang-Mills connections with Weyl structure, J. of Geometry and Physics 60 (2010), 1950-1957.   DOI   ScienceOn
18 J.-S. Park, Projectively flat Yang-Mills connections, Kyushu J. Math. 64 (2010), 49-58.
19 S. Dragomir, T. Ichiyamy and H. Urakawa, Yang-Mills theory and conjugate connections, Differential Geom. Appl. 18 (2003), 229-238.   DOI   ScienceOn