{"title":"罗宾逊-特劳特曼时空中的利玛窦孤子和曲率继承","authors":"Absos Ali Shaikh, Biswa Ranjan Datta","doi":"10.1142/s0219887824501639","DOIUrl":null,"url":null,"abstract":"<p>The purpose of this paper is to investigate the existence of Ricci solitons and the nature of curvature inheritance as well as collineations on the Robinson–Trautman (briefly, RT) spacetime. It is shown that under certain conditions RT spacetime admits almost-Ricci soliton, almost-<span><math altimg=\"eq-00001.gif\" display=\"inline\" overflow=\"scroll\"><mi>η</mi></math></span><span></span>-Ricci soliton, almost-gradient <span><math altimg=\"eq-00002.gif\" display=\"inline\" overflow=\"scroll\"><mi>η</mi></math></span><span></span>-Ricci soliton. As a generalization of curvature inheritance [K. L. Duggal, Curvature inheritance symmetry in Riemannian spaces with applications to fluid space times, <i>J. Math. Phys.</i><b>33</b>(9) (1992) 2989–2997] and curvature collineation [G. H. Katzin, J. Livine and W. R. Davis, Curvature collineations: A fundamental symmetry property of the space-times of general relativity defined by the vanishing Lie derivative of the Riemann curvature tensor, <i>J. Math. Phys.</i><b>10</b>(4) (1969) 617–629], in this paper, we introduce the notion of <i>generalized curvature inheritance</i> and examine if RT spacetime admits such a notion. It is shown that RT spacetime also realizes the generalized curvature (resp., Ricci, Weyl conformal, concircular, conharmonic, Weyl projective) inheritance. Finally, several conditions are obtained, under which RT spacetime possesses curvature (resp., Ricci, conharmonic, Weyl projective) inheritance as well as curvature (resp., Ricci, Weyl conformal, concircular, conharmonic, Weyl projective) collineation, and we have also introduced the concept of generalized Lie inheritance and showed that RT spacetime realizes such a notion.</p>","PeriodicalId":50320,"journal":{"name":"International Journal of Geometric Methods in Modern Physics","volume":"2 1","pages":""},"PeriodicalIF":2.1000,"publicationDate":"2024-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Ricci solitons and curvature inheritance on Robinson–Trautman spacetimes\",\"authors\":\"Absos Ali Shaikh, Biswa Ranjan Datta\",\"doi\":\"10.1142/s0219887824501639\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>The purpose of this paper is to investigate the existence of Ricci solitons and the nature of curvature inheritance as well as collineations on the Robinson–Trautman (briefly, RT) spacetime. It is shown that under certain conditions RT spacetime admits almost-Ricci soliton, almost-<span><math altimg=\\\"eq-00001.gif\\\" display=\\\"inline\\\" overflow=\\\"scroll\\\"><mi>η</mi></math></span><span></span>-Ricci soliton, almost-gradient <span><math altimg=\\\"eq-00002.gif\\\" display=\\\"inline\\\" overflow=\\\"scroll\\\"><mi>η</mi></math></span><span></span>-Ricci soliton. As a generalization of curvature inheritance [K. L. Duggal, Curvature inheritance symmetry in Riemannian spaces with applications to fluid space times, <i>J. Math. Phys.</i><b>33</b>(9) (1992) 2989–2997] and curvature collineation [G. H. Katzin, J. Livine and W. R. Davis, Curvature collineations: A fundamental symmetry property of the space-times of general relativity defined by the vanishing Lie derivative of the Riemann curvature tensor, <i>J. Math. 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引用次数: 0
摘要
本文旨在研究罗宾逊-特劳特曼时空(简称 RT 时空)上利玛窦孤子的存在、曲率继承的性质以及领线。研究表明,在某些条件下,RT 时空存在近似利玛窦孤子、近似η-利玛窦孤子、近似梯度η-利玛窦孤子。作为曲率继承的一般化 [K. L. Duggal, Curvature inheritance] 。L. Duggal, Curvature inheritance symmetry in Riemannian spaces with applications to fluid space times, J. Math. Phys.33(9) (1992).Phys.33(9)(1992)2989-2997] 和曲率邻接[G. H. Katzin, J. Livine and W. R. Davis, Curvature collineations:G. H. Katzin, J. Livine and W. R. Davis, Curvature collineations: A fundamental symmetry property of the space-times of general relativity defined by the vanishing Lie derivative of the Riemann curvature tensor, J. Math. Phys.10(4) (1969).Phys.10(4)(1969)617-629],在本文中,我们引入了广义曲率继承的概念,并研究了 RT 时空是否存在这种概念。结果表明,RT 时空也实现了广义曲率继承(Ricci、Weyl 保角、共圆、共谐、Weyl 投影)。最后,我们得到了几个条件,在这些条件下,RT 时空具有曲率(Ricci、Weyl 保角、协和、Weyl 投射)继承以及曲率(Ricci、Weyl 保角、协圆、协和、Weyl 投射)勾连,我们还引入了广义烈继承的概念,并证明 RT 时空实现了这样一个概念。
Ricci solitons and curvature inheritance on Robinson–Trautman spacetimes
The purpose of this paper is to investigate the existence of Ricci solitons and the nature of curvature inheritance as well as collineations on the Robinson–Trautman (briefly, RT) spacetime. It is shown that under certain conditions RT spacetime admits almost-Ricci soliton, almost--Ricci soliton, almost-gradient -Ricci soliton. As a generalization of curvature inheritance [K. L. Duggal, Curvature inheritance symmetry in Riemannian spaces with applications to fluid space times, J. Math. Phys.33(9) (1992) 2989–2997] and curvature collineation [G. H. Katzin, J. Livine and W. R. Davis, Curvature collineations: A fundamental symmetry property of the space-times of general relativity defined by the vanishing Lie derivative of the Riemann curvature tensor, J. Math. Phys.10(4) (1969) 617–629], in this paper, we introduce the notion of generalized curvature inheritance and examine if RT spacetime admits such a notion. It is shown that RT spacetime also realizes the generalized curvature (resp., Ricci, Weyl conformal, concircular, conharmonic, Weyl projective) inheritance. Finally, several conditions are obtained, under which RT spacetime possesses curvature (resp., Ricci, conharmonic, Weyl projective) inheritance as well as curvature (resp., Ricci, Weyl conformal, concircular, conharmonic, Weyl projective) collineation, and we have also introduced the concept of generalized Lie inheritance and showed that RT spacetime realizes such a notion.
期刊介绍:
This journal publishes short communications, research and review articles devoted to all applications of geometric methods (including commutative and non-commutative Differential Geometry, Riemannian Geometry, Finsler Geometry, Complex Geometry, Lie Groups and Lie Algebras, Bundle Theory, Homology an Cohomology, Algebraic Geometry, Global Analysis, Category Theory, Operator Algebra and Topology) in all fields of Mathematical and Theoretical Physics, including in particular: Classical Mechanics (Lagrangian, Hamiltonian, Poisson formulations); Quantum Mechanics (also semi-classical approximations); Hamiltonian Systems of ODE''s and PDE''s and Integrability; Variational Structures of Physics and Conservation Laws; Thermodynamics of Systems and Continua (also Quantum Thermodynamics and Statistical Physics); General Relativity and other Geometric Theories of Gravitation; geometric models for Particle Physics; Supergravity and Supersymmetric Field Theories; Classical and Quantum Field Theory (also quantization over curved backgrounds); Gauge Theories; Topological Field Theories; Strings, Branes and Extended Objects Theory; Holography; Quantum Gravity, Loop Quantum Gravity and Quantum Cosmology; applications of Quantum Groups; Quantum Computation; Control Theory; Geometry of Chaos.