Characterization of Ricci Solitons and Harmonic Vector Fields on the Lie Group Nil 4

Yanlin Li, Ahmed Mohammed Cherif and Yuquan Xie ()
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Yanlin Li: School of Mathematics, Hangzhou Normal University, Hangzhou 311121, China
Ahmed Mohammed Cherif: Department of Mathematics, University Mustapha Stambouli, Mascara 29000, Algeria
Yuquan Xie: School of Mathematics, Hangzhou Normal University, Hangzhou 311121, China

Mathematics, 2025, vol. 13, issue 7, 1-8

Abstract: This study considers a left-invariant Riemannian metric g on the Lie group N i l 4 . We introduce a Ricci solitons’ classification on ( N i l 4 , g ) . These are expansive non-gradient Ricci solitons. We examine the existence of harmonic maps into ( N i l 4 , g ) from a compact Riemannian manifold. Additionally, we provide a characterization of a class of harmonic vector fields on ( N i l 4 , g ) .

Keywords: Lie groups; Ricci solitons; harmonic maps (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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