Canonical Connections and Algebraic Ricci Solitons of Three-dimensional Lorentzian Lie Groups
In this paper, the author computes canonical connections and Kobayashi-Nomizu connections and their curvature on three-dimensional Lorentzian Lie groups with some product structure. He defines algebraic Ricci solitons associated to canonical connections and Kobayashi-Nomizu connections. He classifie...
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| Published in | Chinese annals of mathematics. Serie B Vol. 43; no. 3; pp. 443 - 458 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Berlin/Heidelberg
Springer Berlin Heidelberg
01.05.2022
Springer Nature B.V School of Mathematics and Statistics,Northeast Normal University,Changchun 130024,China |
| Subjects | |
| Online Access | Get full text |
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| Abstract | In this paper, the author computes canonical connections and Kobayashi-Nomizu connections and their curvature on three-dimensional Lorentzian Lie groups with some product structure. He defines algebraic Ricci solitons associated to canonical connections and Kobayashi-Nomizu connections. He classifies algebraic Ricci solitons associated to canonical connections and Kobayashi-Nomizu connections on three-dimensional Lorentzian Lie groups with some product structure. |
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| AbstractList | In this paper, the author computes canonical connections and Kobayashi-Nomizu connections and their curvature on three-dimensional Lorentzian Lie groups with some product structure. He defines algebraic Ricci solitons associated to canonical connections and Kobayashi-Nomizu connections. He classifies algebraic Ricci solitons associated to canonical connections and Kobayashi-Nomizu connections on three-dimensional Lorentzian Lie groups with some product structure. In this paper,the author computes canonical connections and Kobayashi-Nomizu connections and their curvature on three-dimensional Lorentzian Lie groups with some product structure.He defines algebraic Ricci solitons associated to canonical con-nections and Kobayashi-Nomizu connections.He classifies algebraic Ricci solitons asso-ciated to canonical connections and Kobayashi-Nomizu connections on three-dimensional Lorentzian Lie groups with some product structure. |
| Author | Wang, Yong |
| AuthorAffiliation | School of Mathematics and Statistics,Northeast Normal University,Changchun 130024,China |
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| Cites_doi | 10.1007/s10711-007-9163-7 10.1016/j.geomphys.2016.11.018 10.1016/j.geomphys.2006.10.005 10.5817/AM2016-3-159 10.1007/s10474-014-0426-0 10.1007/PL00004456 |
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| Copyright | The Editorial Office of CAM and Springer-Verlag Berlin Heidelberg 2022 The Editorial Office of CAM and Springer-Verlag Berlin Heidelberg 2022. Copyright © Wanfang Data Co. Ltd. All Rights Reserved. |
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| Keywords | 53C42 53C40 Canonical connections Three-dimensional Lorentzian Lie groups Kobayashi-Nomizu connections Algebraic Ricci solitons |
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| Publisher | Springer Berlin Heidelberg Springer Nature B.V School of Mathematics and Statistics,Northeast Normal University,Changchun 130024,China |
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| References | Lauret (CR6) 2001; 319 Onda (CR7) 2014; 144 Cordero, Parker (CR4) 1997; 17 Batat, Onda (CR1) 2017; 114 Calvaruso (CR3) 2007; 127 Calvaruso (CR2) 2007; 57 Etayo, Santamaria (CR5) 2016; 52 L A Cordero (334_CR4) 1997; 17 J Lauret (334_CR6) 2001; 319 G Calvaruso (334_CR2) 2007; 57 G Calvaruso (334_CR3) 2007; 127 W Batat (334_CR1) 2017; 114 F Etayo (334_CR5) 2016; 52 K Onda (334_CR7) 2014; 144 |
| References_xml | – volume: 127 start-page: 99 year: 2007 end-page: 119 ident: CR3 article-title: Einstein-like metrics on three-dimensional homogeneous Lorentzian manifolds publication-title: Geom. Dedicata doi: 10.1007/s10711-007-9163-7 contributor: fullname: Calvaruso – volume: 114 start-page: 138 year: 2017 end-page: 152 ident: CR1 article-title: Algebraic Ricci solitons of three-dimensional Lorentzian Lie groups publication-title: J. Geom. Phys. doi: 10.1016/j.geomphys.2016.11.018 contributor: fullname: Onda – volume: 17 start-page: 129 issue: 7 year: 1997 end-page: 155 ident: CR4 article-title: Left-invariant Lorentzian metrics on 3-dimensional Lie groups publication-title: Rend. Mat. Appl. contributor: fullname: Parker – volume: 57 start-page: 1279 issue: 4 year: 2007 end-page: 1291 ident: CR2 article-title: Homogeneous structures on three-dimensional Lorentzian manifolds publication-title: J. Geom. Phys. doi: 10.1016/j.geomphys.2006.10.005 contributor: fullname: Calvaruso – volume: 52 start-page: 159 issue: 3 year: 2016 end-page: 203 ident: CR5 article-title: Distinguished connections on ( = ±1)-metric manifolds publication-title: Arch. Math. (Brno) doi: 10.5817/AM2016-3-159 contributor: fullname: Santamaria – volume: 144 start-page: 247 issue: 1 year: 2014 end-page: 265 ident: CR7 article-title: Examples of algebraic Ricci solitons in the pseudo-Riemannian case publication-title: Acta Math. Hungar. doi: 10.1007/s10474-014-0426-0 contributor: fullname: Onda – volume: 319 start-page: 715 issue: 4 year: 2001 end-page: 733 ident: CR6 article-title: Ricci soliton homogeneous nilmanifolds publication-title: Math. Ann. doi: 10.1007/PL00004456 contributor: fullname: Lauret – volume: 144 start-page: 247 issue: 1 year: 2014 ident: 334_CR7 publication-title: Acta Math. Hungar. doi: 10.1007/s10474-014-0426-0 contributor: fullname: K Onda – volume: 17 start-page: 129 issue: 7 year: 1997 ident: 334_CR4 publication-title: Rend. Mat. Appl. contributor: fullname: L A Cordero – volume: 57 start-page: 1279 issue: 4 year: 2007 ident: 334_CR2 publication-title: J. Geom. Phys. doi: 10.1016/j.geomphys.2006.10.005 contributor: fullname: G Calvaruso – volume: 114 start-page: 138 year: 2017 ident: 334_CR1 publication-title: J. Geom. Phys. doi: 10.1016/j.geomphys.2016.11.018 contributor: fullname: W Batat – volume: 319 start-page: 715 issue: 4 year: 2001 ident: 334_CR6 publication-title: Math. Ann. doi: 10.1007/PL00004456 contributor: fullname: J Lauret – volume: 127 start-page: 99 year: 2007 ident: 334_CR3 publication-title: Geom. Dedicata doi: 10.1007/s10711-007-9163-7 contributor: fullname: G Calvaruso – volume: 52 start-page: 159 issue: 3 year: 2016 ident: 334_CR5 publication-title: Arch. Math. (Brno) doi: 10.5817/AM2016-3-159 contributor: fullname: F Etayo |
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| Snippet | In this paper, the author computes canonical connections and Kobayashi-Nomizu connections and their curvature on three-dimensional Lorentzian Lie groups with... In this paper,the author computes canonical connections and Kobayashi-Nomizu connections and their curvature on three-dimensional Lorentzian Lie groups with... |
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| SubjectTerms | Algebra Applications of Mathematics Lie groups Mathematics Mathematics and Statistics Solitary waves |
| Title | Canonical Connections and Algebraic Ricci Solitons of Three-dimensional Lorentzian Lie Groups |
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