Schouten like metrics on five dimensional nilpotents Lie groups
Differential Geometry
2025-05-28 v2
Abstract
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.
Cite
@article{arxiv.2412.20000,
title = {Schouten like metrics on five dimensional nilpotents Lie groups},
author = {Marius Landry Foka and Michel Bertrand Ngaha Djiadeu and Thomas Bouetou Bouetou},
journal= {arXiv preprint arXiv:2412.20000},
year = {2025}
}