Algebraic Schouten solitons of Lorentzian Lie groups with Yano connections

Jinli Yang; Jiajing Miao; Jinli Yang; Jiajing Miao

doi:10.3934/cam.2023037

Communications in Analysis and Mechanics

2023, Volume 15, Issue 4: 763-791. doi: 10.3934/cam.2023037

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Algebraic Schouten solitons of Lorentzian Lie groups with Yano connections

Jinli Yang ,
Jiajing Miao ^,

School of Mathematics, Mudanjiang Normal University, Mudanjiang 157011, P. R. China

Received: 08 June 2023 Revised: 27 October 2023 Accepted: 30 October 2023 Published: 06 November 2023
53C40, 53C42

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} $.
- algebraic Schouten solitons,
- Yano connections,
- Lorentzian Lie groups
Citation: Jinli Yang, Jiajing Miao. Algebraic Schouten solitons of Lorentzian Lie groups with Yano connections[J]. Communications in Analysis and Mechanics, 2023, 15(4): 763-791. doi: 10.3934/cam.2023037

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Abstract

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} $.

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