Marius Landry Foka | Searcharxiv

arXiv2025

Schouten like metrics on five dimensional nilpotents Lie groups

The prescribed Ricci curvature problem involves finding a Riemannian metric g that satisfies the equation ric(g) = T, where T is a fixed symmetric (0, 2)-tensor field on a differential manifold M. In this paper, we introduce the concept of Schouten-like metrics as particular solutions to the prescribed Ricci curvature problem. We classify these metrics on five-dimensional nilpotent Lie groups by establishing a connection with algebraic Schouten solitons. This approach also enables us to classify five-dimensional nilsolitons, providing a comprehensive understanding of their geometric structures and properties.

math.DG↗

arXiv2024

The prescribed Ricci curvature problem on 5-dimensional nilpotent Lie groups

In this paper, using the Milnor-type theorem technique, we provide on each nilpotent five dimensional Lie group, some global existence result of a pair (g, c) consisting of a left-invariant Riemannian metric g and a positive constant c such that Ric(g) =cT, where Ric(g) is the Ricci curvature of g and T a given left-invariant symmetric (0, 2)-tensor field.

math.DG↗