Characterization of Ricci Solitons and Harmonic Vector Fields on the Lie Group Nil4 - Yanlin Li; Ahmed Mohammed Cherif; Yuquan Xie (Mathematics)
This study considers a left-invariant Riemannian metric g on the Lie group <semantics>Nil4</semantics>. We introduce a Ricci solitons’ classification on <semantics>(Nil4,g)</semantics>. These are expansive non-gradient Ricci solitons. We examine the existence of harmonic maps into <semantics>(Nil4,g)</semantics> from a compact Riemannian manifold. Additionally, we provide a characterization of a class of harmonic vector fields on <semantics>(Nil4,g)</semantics>.