Schouten-like Metrics on Five-Dimensional Nilpotent Lie Groups

Year 2025, Volume: 18 Issue: 2, 384 - 395

Marius Landry Foka , Michel Bertrand Ngaha Djiadeu , Thomas Bouetou Bouetou

https://doi.org/10.36890/iejg.1706246

Abstract

The prescribed Ricci curvature problem consists of finding a Riemannian metric $g$ to satisfy the equation $Ric(g) = T$, for some fixed symmetric $(0,2)$-tensor field $T$ on a differential manifold $M$. In this paper, we define Schouten-like metric as a particular solution of a prescribed Ricci curvature problem, and we classify them on five-dimensional nilpotent Lie groups by establishing a link with algebraic Schouten solitons.

Keywords

Lie group , Lie algebra , Ricci operator , nilsoliton , algebraic Schouten soliton , Schouten-like metric

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