Schouten like metrics on five dimensional nilpotents Lie groups

TL;DR

This paper introduces Schouten-like metrics on five-dimensional nilpotent Lie groups, classifies them via algebraic Schouten solitons, and advances understanding of nilsoliton structures in differential geometry.

Contribution

It establishes a new class of solutions to the prescribed Ricci curvature problem and classifies five-dimensional nilpotent Lie group metrics using algebraic Schouten solitons.

Findings

Classification of Schouten-like metrics on five-dimensional nilpotent Lie groups

Connection between Schouten-like metrics and algebraic Schouten solitons

Comprehensive classification of five-dimensional nilsolitons

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.