HARMONIC MAPS BETWEEN THE GROUP OF AUTOMORPHISMS OF THE QUATERNION ALGEBRA

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Published: May 15, 2012
DOI: https://doi.org/10.14403/jcms.2012.25.2.331
Keywords:
harmonic map, Killing form, semisimple Lie group, invariant Riemannian metric
Mathematics Subject Classification (2020):
Primary 53C07, 53C25

Main Article Content

Pu-Young Kim
Department of Applied Mathematics, Pukyong National University
Joon-Sik Park
Department of Mathematics, Pusan University of Foreign Studies
Yong-Soo Pyo
Department of Applied Mathematics, Pukyong National University

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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Article Details

Issue
Vol. 25 No. 2 (2012)
Section
Articles