Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
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HARMONIC MAPS BETWEEN THE GROUP OF AUTOMORPHISMS OF THE QUATERNION ALGEBRA

  • Kim, Pu-Young (Department of Applied Mathematics Pukyong National University) ;
  • Park, Joon-Sik (Department of Mathematics Pusan University of Foreign Studies) ;
  • Pyo, Yong-Soo (Department of Applied Mathematics Pukyong National University)
  • Published : 2012.05.15
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Abstract

In this paper, let Q be the real quaternion algebra which consists of all quaternionic numbers, and let G be the Lie group of all automorphisms of the algebra Q. Assume that g is an arbitrary given left invariant Riemannian metric on the Lie group G. Then, we obtain a necessary and sufficient condition for an automorphism of the group G to be harmonic.

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References

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  1. A DECOMPOSITION OF THE CURVATURE TENSOR ON SU(3)=T (k, l) WITH A SU(3)-INVARIANT METRIC vol.28, pp.2, 2015, https://doi.org/10.14403/jcms.2015.28.2.229
  2. Harmonic and biharmonic homomorphisms between Riemannian Lie groups vol.116, 2017, https://doi.org/10.1016/j.geomphys.2017.01.003