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HARMONIC HOMOMORPHISMS BETWEEN TWO LIE GROUPS
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  • Journal title : Honam Mathematical Journal
  • Volume 38, Issue 1,  2016, pp.1-8
  • Publisher : The Honam Mathematical Society
  • DOI : 10.5831/HMJ.2016.38.1.1
 Title & Authors
HARMONIC HOMOMORPHISMS BETWEEN TWO LIE GROUPS
Son, Heui-Sang; Kim, Hyun Woong; Park, Joon-Sik;
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 Abstract
In this paper, we get a complete condition for a group homomorphism of a compact Lie group with an arbitrarily given left invariant Riemannian metric into another Lie group with a left invariant metric to be a harmonic map, and then obtain a necessary and sufficient condition for a group homomorphism of (SU(2), g) with a left invariant metric g into the Heisenberg group (H, ) to be a harmonic map.
 Keywords
Lie group;group homomorphism;left invariant metric;Heisenberg group;
 Language
English
 Cited by
 References
1.
H. W. Kim, Y.-S. Pyo and H.-J. Shin, Ricci and scalar curvatures on SU(3), Honam Math. J., 34(2) 2012), 231-239. crossref(new window)

2.
S. Kobayashi and K. Nomizu, Foundations of Differential Geometry, Vol. I, Interscience Pub., 1963.

3.
J.-S. Park, Yang-Mills connections in orthonormal frame bundles over SU(2), Tsukuba J. Math., 18 (1994), 203-206.

4.
J.-S. Park, Critical homogeneous metrics on the Heisenberg manifold, Int. Inform. Sci., 11 (2005), 31-34.

5.
J.-S. Park and W. T. Oh, The Abbena-Thurston manifold as a critical point, Can. Math. Bull., 39 (1996), 352-359. crossref(new window)

6.
K. Sugahara, The sectional curvature and the diameter estimate for the left invariant metrics on SU(2, ${\mathbb{C}}$) and SO(3, ${\mathbb{R}}$), Math. Japonica, 26 (1981), 153-159.

7.
H. Urakawa, Calculus of variations and harmonic Maps, Amer. Math. Soc., Providence, Rhode Island, 1993.