Algebraic Schouten solitons of Lorentzian Lie groups with Yano connections

Abstract

<abstract><p>In this paper, we discuss the beingness conditions for algebraic Schouten solitons associated with Yano connections in the background of three-dimensional Lorentzian Lie groups. By transforming equations of algebraic Schouten solitons into algebraic equations, the existence conditions of solitons are found. In particular, we deduce some formulations for Yano connections and related Ricci operators. Furthermore, we find the detailed categorization for those algebraic Schouten solitons on three-dimensional Lorentzian Lie groups. The major results demonstrate that algebraic Schouten solitons related to Yano connections are present in $ G_{1} $, $ G_{2} $, $ G_{3} $, $ G_{5} $, $ G_{6} $ and $ G_{7} $, while they are not identifiable in $ G_{4} $.</p></abstract>