isoparametric functions
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2020 ◽  
Vol 58 (4) ◽  
pp. 477-496
Author(s):  
Sigmundur Gudmundsson ◽  
Marko Sobak

Abstract In this paper we introduce the notion of complex isoparametric functions on Riemannian manifolds. These are then employed to devise a general method for constructing proper r-harmonic functions. We then apply this to construct the first known explicit proper r-harmonic functions on the Lie group semidirect products $${{\mathbb {R}}}^m \ltimes {{\mathbb {R}}}^n$$ R m ⋉ R n and $${{\mathbb {R}}}^m \ltimes \mathrm {H}^{2n+1}$$ R m ⋉ H 2 n + 1 , where $$\mathrm {H}^{2n+1}$$ H 2 n + 1 denotes the classical $$(2n+1)$$ ( 2 n + 1 ) -dimensional Heisenberg group. In particular, we construct such examples on all the simply connected irreducible four-dimensional Lie groups.



2019 ◽  
Vol 74 (4) ◽  
Author(s):  
Wenjing Hao ◽  
Xingxiao Li




2018 ◽  
Vol 60 ◽  
pp. 1-8
Author(s):  
Jurgen Julio-Batalla






2015 ◽  
Vol 272 ◽  
pp. 611-629 ◽  
Author(s):  
Chao Qian ◽  
Zizhou Tang


2014 ◽  
Vol 21 (4) ◽  
pp. 257-270
Author(s):  
Seo-In Jee ◽  
Jae-Hyouk Lee




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