Algebraic Schouten Solitons of Three-Dimensional Lorentzian Lie Groups

TL;DR

This paper classifies algebraic Schouten solitons, a special type of T-soliton, on three-dimensional Lorentzian Lie groups with various connections, expanding understanding of geometric structures in Lorentzian geometry.

Contribution

It introduces the concept of algebraic Schouten solitons as a specific T-soliton and provides a classification on three-dimensional Lorentzian Lie groups for different connections.

Findings

Classification of algebraic Schouten solitons on Lorentzian Lie groups.

Extension of T-soliton theory to Schouten solitons.

Analysis of solitons related to various connections.

Abstract

In [10], Wears defined and studied algebraic T-solitons. In this paper, we give the definition of algebraic Schouten solitons as a special T-soliton and classify algebraic Schouten solitons associated to Levi-Civita connections, canonical connections and Kobayashi-Nomizu connections on three-dimensional Lorentzian Lie groups with some product structure.