Algebraic Schouten solitons associated to the Bott connection on three-dimensional Lorentzian Lie groups

Electronic Research Archive ›› 2025, Vol. 33 ›› Issue (1) : 327 -352.

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Electronic Research Archive ›› 2025, Vol. 33 ›› Issue (1) :327 -352. DOI: 10.3934/era.2025017
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Algebraic Schouten solitons associated to the Bott connection on three-dimensional Lorentzian Lie groups
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Abstract

In this paper, I define and classify the algebraic Schouten solitons associated with the Bott connection on three-dimensional Lorentzian Lie groups with three different distributions.

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Jinguo Jiang. Algebraic Schouten solitons associated to the Bott connection on three-dimensional Lorentzian Lie groups. Electronic Research Archive, 2025, 33 (1) : 327-352 DOI:10.3934/era.2025017

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References

[1]

R. S. Hamilton, The Ricci flow on surfaces, in mathematics and general relativity, Contemp. Math., 71 (1988), 237-261. https://doi.org/10.1090/conm/071/954419

[2]

G. Perelman, The entropy formula for the ricci flow and its geometric applications, preprint, arXiv:math/0211159. https://doi.org/10.48550/arXiv.math/0211159

[3]

J. Lauret, Ricci soliton homogeneous nilmanifolds, Math. Ann., 319 (2001), 715-733. https://doi.org/10.1007/PL00004456

[4]

W. Batat, K. Onda, Algebraic Ricci solitons of three-dimensional Lorentzian Lie groups, J. Geom. Phys., 114 (2017), 138-152. https://doi.org/10.1016/j.geomphys.2016.11.018

[5]

F. Etayo, R. Santamaría, Distinguished connections on (J2 = ±1)-metric manifolds , Arch. Math., 52 (2016), 159-203. https://doi.org/10.5817/AM2016-3-159

[6]

Y. Wang, Canonical connections and algebraic Ricci solitons of three-dimensional Lorentzian Lie groups, Chin. Ann. Math. Ser. B, 43 (2022), 443-458. https://doi.org/10.1007/s11401-022-0334-5

[7]

S. Azami, Generalized Ricci solitons of three-dimensional Lorentzian Lie groups associated canonical connections and Kobayashi-Nomizu connections, J. Nonlinear Math. Phys., 30 (2023), 1-33. https://doi.org/10.1007/s44198-022-00069-2

[8]

S. Azami, Generalized Ricci solitons associated to perturbed canonical connection and perturbed Kobayashi-Nomizu connection on three-dimensional Lorentzian Lie groups, Afr. Mat., 35 (2024), 36. https://doi.org/10.1007/s13370-024-01184-7

[9]

J. A. Alvarez López, P. Tondeur, Hodge decomposition along the leaves of a Riemannian foliation, J. Funct. Anal., 99 (1991), 443-458. https://doi.org/10.1016/0022-1236(91)90048-A

[10]

F. Baudoin, Sub-Laplacians and hypoelliptic operators on totally geodesic Riemannian foliations, in Geometry, Analysis and Dynamics on Sub-Riemannian Manifolds, 1 (2016), 259-321. https://doi.org/10.4171/162-1/3

[11]

R. K. Hladky, Connections and curvature in sub-Riemannian geometry, Houston J. Math., 38 (2012), 1107-1134.

[12]

F. Baudoin, E. Grong, K. Kuwada, A. Thalmaier, Sub-Laplacian comparison theorems on totally geodesic Riemannian foliations, Calc. Var. Partial Differ. Equations, 58 (2019), 1308. https://doi.org/10.1007/s00526-019-1570-8

[13]

T. Wu, Y. Wang, Affine Ricci solitons associated to the Bott connection on three-dimensional Lorentzian Lie groups, Turkish J. Math., 45 (2021), 2773-2816. https://doi.org/10.3906/mat-2105-49

[14]

J. Yang, J. Miao, Algebraic Schouten solitons of Lorentzian Lie groups with Yano connections, Commun. Anal. Mech., 15 (2023), 763-791. https://doi.org/10.3934/cam.2023037

[15]

S. Liu, Algebraic schouten solitons of three-dimensional lorentzian lie groups, Symmetry, 15 (2023), 866. https://doi.org/10.3390/sym15040866

[16]

T. H. Wears, On algebraic solitons for geometric evolution equations on three-dimensional Lie groups, Tbilisi Math. J., 9 (2016), 33-58. https://doi.org/10.1515/tmj-2016-0018

[17]

J. Milnor, Curvatures of left invariant metrics on Lie groups, Adv. Math., 21 (1976), 293-329. https://doi.org/10.1016/S0001-8708(76)80002-3

[18]

S. Rahmani, Métriques de Lorentz sur les groupes de Lie unimodulaires, de dimension trois, J. Geom. Phys., 9 (1992), 295-302. https://doi.org/10.1016/0393-0440(92)90033-W

[19]

G. Calvaruso, Homogeneous structures on three-dimensional Lorentzian manifolds, J. Geom. Phys., 57 (2017), 1279-1291. https://doi.org/10.1016/j.geomphys.2006.10.005

[20]

L. A. Cordero, P. E. Parker, Left-invariant Lorentzian metrics on 3-dimensional Lie groups, Rend. Mat. Appl., 17 (1997), 129-155.

[21]

A. Derdziński, C. L. Shen, Codazzi tensor fields, curvature and Pontryagin forms, Proc. London Math. Soc., 47 (1983), 15-26. https://doi.org/10.1112/plms/s3-47.1.15

[22]

H. R. Salimi Moghaddam, On the geometry of some para-hypercomplex Lie groups, Arch. Math., 45 (2009), 159-170.

[23]

G. F. Ramandi, S. Azami, V. Pirhadi, Generalized lorentzian Ricci solitons on 3-dimensional Lie groups associated to the Bott Connection, AUT J. Math. Comput., 5 (2024), 305-319. https://doi.org/10.22060/AJMC.2023.22329.1153

[24]

R. B. Chamazkoti, Lorentz Ricci solitons of four-dimensional non-Abelian nilpotent Lie groups, Mediterr. J. Math., 19 (2022), 111. https://doi.org/10.1007/s00009-022-02024-3

[25]

S. Azami, G. Fasihi-Ramandi, V. Pirhadi, Generalized Ricci solitons on non-reductive four-dimensional homogeneous spaces, J. Nonlinear Math. Phys., 30 (2023), 1069-1093. https://doi.org/10.1007/s44198-023-00116-6

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