一类新的伪黎曼可解代数里奇孤立子
A New Class of Pseudo-Riemannian Solvable Algebraic Ricci Solitons
摘要: 里奇孤立子是一类重要的黎曼度量，它是一类重要的哈密尔顿曲率流的解，有重要的几何性质，具有重要的理论研究价值。在本文中，我们研究了在可解连通李群上构造伪黎曼代数里奇孤立子的一般方法，并在可解李群上构造了伪黎曼代数里奇孤立子，给出了它们等距的充分必要条件。
Abstract: Ricci soliton is an important Riemannian metric, which is an important solution of the Hamilton curvature flow. So Ricci soliton has important geometry properties and significant research values. In this paper, we study the generally method of constructing pseudo Riemannian algebraic soliton on solvable connected Lie group, and we get the pseudo Riemannian algebraic soliton. Besides, we give the sufficient and necessary conditions in which two pseudo Riemannian algebraic soliton are isometrical to each other.
文章引用：黄浩, 王辉. 一类新的伪黎曼可解代数里奇孤立子[J]. 应用数学进展, 2023, 12(7): 3121-3126. https://doi.org/10.12677/AAM.2023.127311

参考文献

[1] Lauret, J. (2001) Ricci Soliton Homogeneous Nilmanifolds. Mathematische Annalen, 319, 715-733. [Google Scholar] [CrossRef] 
[2] Lauret, J. (2002) Finding Einstein Solvmanifolds by a Variational Meth-od. Mathematische Zeitschrift, 241, 83-99. [Google Scholar] [CrossRef] 
[3] Lauret, J. (2011) Ricci Soliton Solvmanifolds. Journal für die reine und angewandte Mathematik, 2011, 1-21. [Google Scholar] [CrossRef] 
[4] Lauret, J. and Will, C. (2011) Einstein Solvmanifolds: Existence and Non-Existence Questions. Mathematische Annalen, 350, 199-225. [Google Scholar] [CrossRef] 
[5] Nikolayevsky, Y. (2011) Einstein Solvmanifolds and the Pre-Einstein Derivation. Transactions of the American Mathematical Society, 363, 3935-3958. [Google Scholar] [CrossRef] 
[6] Bajo, I., Benayadi, S. and Medina, A. (2007) Symplectic Structures on Quadratic Lie Algebras. Journal of Algebra, 316, 174-188. [Google Scholar] [CrossRef] 
[7] Barco, V.D. and Ovando, G.P. (2012) Free Nilpotent Lie Alge-bras Admitting Ad-Invariant Metrics. Journal of Algebra, 366, 205-216. [Google Scholar] [CrossRef] 
[8] Benayadi, S. and Elduqe, A. (2014) Classification of Quadratic Lie Algebras of Low Dimension. Journal of Mathematical Physics, 55, Article ID: 0811703. [Google Scholar] [CrossRef] 
[9] Bordemann, M. (1997) Nondegenerate Invariant Bilinear Forms on Nonassociative Algebras. Acta Mathematica Universitatis Comenianae, 66, 151-201.
[10] Chen, S. and Liang, K. (2012) Left-Invariant Pseudo-Einstein Metrics on Lie Groups. Journal of Nonlinear Mathematical Physics, 19, 236-246. [Google Scholar] [CrossRef] 
[11] Conti, D. and Rossi, F.A. (2019) Einstein Nilpotent Lie Groups. Journal of Pure and Applied Algebra, 223, 976-997. [Google Scholar] [CrossRef] 
[12] Conti, D. and Rossi, F.A. (2019) Ricci-Flat and Einstein Pseu-doriemannian Nilmanifolds. Complex Manifolds, 6, 170-193. [Google Scholar] [CrossRef] 
[13] Derdzinski, A. and Gal, S.R. (2014) Indefinite Einstein Metrics on Simple Lie Group. Indiana University Mathematics Journal, 63, 165-212. [Google Scholar] [CrossRef] 
[14] Duong, M.T., Pinczon, G. and Ushirobira, R. (2012) A New In-variant of Quadratic Lie Algebras. Algebras and Representation Theory, 15, 1163-1203. [Google Scholar] [CrossRef] 
[15] Favre, G. and Santharoubane, L.J. (1987) Symmetric, Invariant, Non-Degenerate Bilinear Form on a Lie Algebra. Journal of Algebra, 105, 451-464. [Google Scholar] [CrossRef] 
[16] Figueroa-O’Farrill, J. and Stanciu, S. (1996) On the Structure of Symmetric Self-Dual Lie Algebras. Journal of Mathematical Physics, 37, 4121-4134. [Google Scholar] [CrossRef] 
[17] Onda, K. (2010) Lorentz Ricci Solitons on 3-Dimensional Lie Groups. Ge-ometriae Dedicata, 147, 313-322. [Google Scholar] [CrossRef] 
[18] Rahmani, S. (1992) Metriques de Lorentz sur les groupes de Lie unimodulaires, de dimension trois [Lorentz Metrics on Three-Dimensional Unimodular Lie Groups]. Journal of Geome-try and Physics, 9, 295-302. [Google Scholar] [CrossRef] 
[19] Onda, K. (2014) Example of Algebraic Ricci Solitons in the Pseudo-Riemannian Case. Acta Mathematica Hungarica, 144, 247-265. [Google Scholar] [CrossRef] 
[20] Yan, Z.L. and Deng, S.Q. (2021) Double Extensions on Rie-mannian Ricci Nilsolitons. The Journal of Geometric Analysis, 31, 9996-10023. [Google Scholar] [CrossRef] 
[21] Heber, J. (1998) Noncompact Homogeneous Einstein Spaces. Inventiones Mathematicae, 133, 279-352. [Google Scholar] [CrossRef] 
[22] Zhang, H. and Yan, Z.L. (2021) New Pseudo Einstein Metrics on Einstein Solvmanifolds. Manuscripta Mathematica, 166, 427-436. [Google Scholar] [CrossRef] 

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