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Symmetry
Volume 17
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10.3390/sym17010010
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Article

Classification of Algebraic Schouten Solitons on Lorentzian Lie Groups Associated with the Perturbed Canonical Connection and the Perturbed Kobayashi–Nomizu Connection

by
Jinguo Jiang
and
Yanni Yang
*
School of Mathematical Science, Nankai University, Tianjin 300071, China
*
Author to whom correspondence should be addressed.
Symmetry 2025, 17(1), 10; https://doi.org/10.3390/sym17010010
Submission received: 3 December 2024 / Revised: 21 December 2024 / Accepted: 23 December 2024 / Published: 25 December 2024
(This article belongs to the Section Mathematics)
Versions Notes

Abstract

In this paper, we investigate the algebraic conditions of algebraic Schouten solitons on three-dimensional Lorentzian Lie groups associated with the perturbed canonical connection and the perturbed Kobayashi–Nomizu connection. Furthermore, we provide the complete classification for these algebraic Schouten solitons on three-dimensional Lorentzian Lie groups associated with the algebraic Schouten solitons. The main results indicate that G4 does not possess algebraic Schouten solitons related to the perturbed Kobayashi–Nomizu connection, G1,G2,G3,G6, and G7 possess algebraic Schouten solitons, and the result for G5 is trivial.
Keywords: pseudo-Riemannian metric; algebraic Schouten solitons; Lorentzian Lie groups pseudo-Riemannian metric; algebraic Schouten solitons; Lorentzian Lie groups

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MDPI and ACS Style

Jiang, J.; Yang, Y. Classification of Algebraic Schouten Solitons on Lorentzian Lie Groups Associated with the Perturbed Canonical Connection and the Perturbed Kobayashi–Nomizu Connection. Symmetry 2025, 17, 10. https://doi.org/10.3390/sym17010010

AMA Style

Jiang J, Yang Y. Classification of Algebraic Schouten Solitons on Lorentzian Lie Groups Associated with the Perturbed Canonical Connection and the Perturbed Kobayashi–Nomizu Connection. Symmetry. 2025; 17(1):10. https://doi.org/10.3390/sym17010010

Chicago/Turabian Style

Jiang, Jinguo, and Yanni Yang. 2025. "Classification of Algebraic Schouten Solitons on Lorentzian Lie Groups Associated with the Perturbed Canonical Connection and the Perturbed Kobayashi–Nomizu Connection" Symmetry 17, no. 1: 10. https://doi.org/10.3390/sym17010010

APA Style

Jiang, J., & Yang, Y. (2025). Classification of Algebraic Schouten Solitons on Lorentzian Lie Groups Associated with the Perturbed Canonical Connection and the Perturbed Kobayashi–Nomizu Connection. Symmetry, 17(1), 10. https://doi.org/10.3390/sym17010010

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