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arXiv · 1812.02777

New biharmonic functions on the compact Lie groups $SO(n)$, $SU(n)$, $Sp(n)$

Sigmundur Gudmundsson·Anna Siffert
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Abstract

We develope a new scheme for the construction of explicit complex-valued proper biharmonic functions on Riemannian Lie groups. We exploit this and manufacture many infinite series of uncountable families of new solutions on the special unitary group $SU(n)$. We then show that the special orthogonal group $SO(n)$ and the quaternionic unitary group $Sp(n)$ fall into the scheme. As a by-product we obtain new harmonic morphisms on these groups. All the constructed maps are defined on open and dense subsets of the corresponding spaces.

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Sigmundur Gudmundsson, Anna Siffert. 2018-12-06. New biharmonic functions on the compact Lie groups $SO(n)$, $SU(n)$, $Sp(n)$. https://arxiv.org/abs/1812.02777

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