# HARMONIC HOMOMORPHISMS BETWEEN TWO LIE GROUPS

• Son, Heui-Sang (Department of Applied Mathematics, Pukyong National University) ;
• Kim, Hyun Woong (Department of Applied Mathematics, Pukyong National University) ;
• Park, Joon-Sik (Department of Mathematics, Pusan University of Foreign Studies)
• Received : 2015.03.16
• Accepted : 2015.12.16
• Published : 2016.03.25
• 94 14

#### 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, $h_0$) to be a harmonic map.

#### Keywords

Lie group;group homomorphism;left invariant metric;Heisenberg group

#### References

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