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Journal of Geometric Mechanics最新文献

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A family of multiply warped product semi-Riemannian Einstein metrics 一组多重翘曲积半黎曼爱因斯坦度量
IF 0.8 4区 数学
Journal of Geometric Mechanics Pub Date : 2020-01-01 DOI: 10.3934/jgm.2020017
B. Pal, Pankaj Kumar
{"title":"A family of multiply warped product semi-Riemannian Einstein metrics","authors":"B. Pal, Pankaj Kumar","doi":"10.3934/jgm.2020017","DOIUrl":"https://doi.org/10.3934/jgm.2020017","url":null,"abstract":"In this paper, we characterize multiply warped product semi -Riemannian manifolds when the base is conformal to an begin{document}$ n $end{document} -dimensional pseudo-Euclidean space. We prove some conditions on warped product semi- Riemannian manifolds to be an Einstein manifold which is invariant under the action of an begin{document}$ (n-1) $end{document} -dimensional translation group. After that we apply this result for the case of Ricci-flat multiply warped product space when the fibers are Ricci-flat. We also discuss the existence of infinitely many Ricci-flat multiply warped product spaces under the same action with null like vector.","PeriodicalId":49161,"journal":{"name":"Journal of Geometric Mechanics","volume":"19 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86039280","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
Erratum for 'nonholonomic and constrained variational mechanics' “非完整和受限变分力学”的勘误
IF 0.8 4区 数学
Journal of Geometric Mechanics Pub Date : 2020-01-01 DOI: 10.3934/jgm.2020033
A. D. Lewis
{"title":"Erratum for 'nonholonomic and constrained variational mechanics'","authors":"A. D. Lewis","doi":"10.3934/jgm.2020033","DOIUrl":"https://doi.org/10.3934/jgm.2020033","url":null,"abstract":"There is an error in the statement of Theorem 4.25 in [1], a somewhat related typographical error in Remark 4.26, and an error in Remark 4.27 following directly from that in Theorem 4.25. Footnote 8 is also now obsolete. In order to ensure that the errors are unambiguously fixed, what appears below should replace the original text starting from just before the statement of Theorem 4.25 and ending at the end of Section 4.","PeriodicalId":49161,"journal":{"name":"Journal of Geometric Mechanics","volume":"11 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87041492","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Invariant structures on Lie groups 李群上的不变结构
IF 0.8 4区 数学
Journal of Geometric Mechanics Pub Date : 2020-01-01 DOI: 10.3934/jgm.2020007
J. P. Álvarez
{"title":"Invariant structures on Lie groups","authors":"J. P. Álvarez","doi":"10.3934/jgm.2020007","DOIUrl":"https://doi.org/10.3934/jgm.2020007","url":null,"abstract":"We approach with geometrical tools the contactization and symplectization of filiform structures and define Hamiltonian structures and momentum mappings on Lie groups.","PeriodicalId":49161,"journal":{"name":"Journal of Geometric Mechanics","volume":"5 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89244001","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Angular momentum coupling, Dirac oscillators, and quantum band rearrangements in the presence of momentum reversal symmetries 角动量耦合，狄拉克振子，以及动量反转对称性下的量子带重排
IF 0.8 4区 数学
Journal of Geometric Mechanics Pub Date : 2020-01-01 DOI: 10.3934/jgm.2020021
T. Iwai, D. Sadovskií, B. Zhilinskií
{"title":"Angular momentum coupling, Dirac oscillators, and quantum band rearrangements in the presence of momentum reversal symmetries","authors":"T. Iwai, D. Sadovskií, B. Zhilinskií","doi":"10.3934/jgm.2020021","DOIUrl":"https://doi.org/10.3934/jgm.2020021","url":null,"abstract":"We investigate the elementary rearrangements of energy bands in slow-fast one-parameter families of systems whose fast subsystem possesses a half-integer spin. Beginning with a simple case without any time-reversal symmetries, we analyze and compare increasingly sophisticated model Hamiltonians with these symmetries. The models are inspired by the time-reversal modification of the Berry phase setup which uses a family of quadratic spin-quadrupole Hamiltonians of Mead [Phys. Rev. Lett. 59, 161–164 (1987)] and Avron et al [Commun. Math. Phys. 124(4), 595–627 (1989)]. An explicit correspondence between the typical quantum energy level patterns in the energy band rearrangements of the finite particle systems with compact slow phase space and those of the Dirac oscillator is found in the limit of linearization near the conical degeneracy point of the semi-quantum eigenvalues.","PeriodicalId":49161,"journal":{"name":"Journal of Geometric Mechanics","volume":"13 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88468258","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
The group of symplectic birational maps of the plane and the dynamics of a family of 4D maps 平面的辛双国图群和四维图族的动力学
IF 0.8 4区 数学
Journal of Geometric Mechanics Pub Date : 2020-01-01 DOI: 10.3934/jgm.2020010
I. Cruz, H. Mena-Matos, Esmeralda Sousa-Dias
{"title":"The group of symplectic birational maps of the plane and the dynamics of a family of 4D maps","authors":"I. Cruz, H. Mena-Matos, Esmeralda Sousa-Dias","doi":"10.3934/jgm.2020010","DOIUrl":"https://doi.org/10.3934/jgm.2020010","url":null,"abstract":"We consider a family of birational maps begin{document}$ varphi_k $end{document} in dimension 4, arising in the context of cluster algebras from a mutation-periodic quiver of period 2. We approach the dynamics of the family begin{document}$ varphi_k $end{document} using Poisson geometry tools, namely the properties of the restrictions of the maps begin{document}$ varphi_k $end{document} and their fourth iterate begin{document}$ varphi^{(4)}_k $end{document} to the symplectic leaves of an appropriate Poisson manifold begin{document}$ (mathbb{R}^4_+, P) $end{document} . These restricted maps are shown to belong to a group of symplectic birational maps of the plane which is isomorphic to the semidirect product begin{document}$ SL(2, mathbb{Z})ltimesmathbb{R}^2 $end{document} . The study of these restricted maps leads to the conclusion that there are three different types of dynamical behaviour for begin{document}$ varphi_k $end{document} characterized by the parameter values begin{document}$ k = 1 $end{document} , begin{document}$ k = 2 $end{document} and begin{document}$ kgeq 3 $end{document} .","PeriodicalId":49161,"journal":{"name":"Journal of Geometric Mechanics","volume":"270 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76564243","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The method of averaging for Poisson connections on foliations and its applications 叶上泊松连接的平均方法及其应用
IF 0.8 4区 数学
Journal of Geometric Mechanics Pub Date : 2020-01-01 DOI: 10.3934/jgm.2020015
M. Avendaño-Camacho, Isaac Hasse-Armengol, E. Velasco-Barreras, Y. Vorobiev
{"title":"The method of averaging for Poisson connections on foliations and its applications","authors":"M. Avendaño-Camacho, Isaac Hasse-Armengol, E. Velasco-Barreras, Y. Vorobiev","doi":"10.3934/jgm.2020015","DOIUrl":"https://doi.org/10.3934/jgm.2020015","url":null,"abstract":"On a Poisson foliation equipped with a canonical and cotangential action of a compact Lie group, we describe the averaging method for Poisson connections. In this context, we generalize some previous results on Hannay-Berry connections for Hamiltonian and locally Hamiltonian actions on Poisson fiber bundles. Our main application of the averaging method for connections is the construction of invariant Dirac structures parametrized by the 2-cocycles of the de Rham-Casimir complex of the Poisson foliation.","PeriodicalId":49161,"journal":{"name":"Journal of Geometric Mechanics","volume":"12 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78290931","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Continuous singularities in hamiltonian relative equilibria with abelian momentum isotropy 具有阿贝尔动量各向同性的哈密顿相对平衡中的连续奇点
IF 0.8 4区 数学
Journal of Geometric Mechanics Pub Date : 2020-01-01 DOI: 10.3934/jgm.2020019
M. Rodríguez-Olmos
{"title":"Continuous singularities in hamiltonian relative equilibria with abelian momentum isotropy","authors":"M. Rodríguez-Olmos","doi":"10.3934/jgm.2020019","DOIUrl":"https://doi.org/10.3934/jgm.2020019","url":null,"abstract":"We survey several aspects of the qualitative dynamics around Hamiltonian relative equilibria. We pay special attention to the role of continuous singularities and its effect in their stability, persistence and bifurcations. Our approach is semi-global using extensively the Hamiltonian tube of Marle, Guillemin and Sternberg.","PeriodicalId":49161,"journal":{"name":"Journal of Geometric Mechanics","volume":"7 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78727675","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Generalised Kähler structure on $ mathbb{C}P^2 $ and elliptic functions $ mathbb{C}P^2 $和椭圆函数上的广义Kähler结构
IF 0.8 4区 数学
Journal of Geometric Mechanics Pub Date : 2019-11-28 DOI: 10.3934/jgm.2023009
F. Bonechi, J. Qiu, M. Tarlini
{"title":"Generalised Kähler structure on $ mathbb{C}P^2 $ and elliptic functions","authors":"F. Bonechi, J. Qiu, M. Tarlini","doi":"10.3934/jgm.2023009","DOIUrl":"https://doi.org/10.3934/jgm.2023009","url":null,"abstract":"We construct a toric generalised Kähler structure on $ mathbb{C}P^2 $ and show that the various structures such as the complex structure, metric etc are expressed in terms of certain elliptic functions. We also compute the generalised Kähler potential in terms of integrals of elliptic functions.","PeriodicalId":49161,"journal":{"name":"Journal of Geometric Mechanics","volume":"39 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2019-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76395797","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Characterization of toric systems via transport costs 通过运输成本表征环形系统
IF 0.8 4区 数学
Journal of Geometric Mechanics Pub Date : 2019-09-15 DOI: 10.3934/jgm.2020027
Sonja Hohloch
{"title":"Characterization of toric systems via transport costs","authors":"Sonja Hohloch","doi":"10.3934/jgm.2020027","DOIUrl":"https://doi.org/10.3934/jgm.2020027","url":null,"abstract":"We characterize completely integrable Hamiltonian systems inducing an effective Hamiltonian torus action as systems with zero transport costs w.r.t. the time-$T$ map where $T in {mathbb R}^n$ is the period of the acting $n$-torus.","PeriodicalId":49161,"journal":{"name":"Journal of Geometric Mechanics","volume":"8 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2019-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74341204","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Relative periodic solutions of the begin{document}$ n $end{document}-vortex problem on the sphere Relative periodic solutions of the begin{document}$ n $end{document}-vortex problem on the sphere
IF 0.8 4区 数学
Journal of Geometric Mechanics Pub Date : 2019-08-21 DOI: 10.3934/JGM.2019021
C. García-Azpeitia
{"title":"Relative periodic solutions of the begin{document}$ n $end{document}-vortex problem on the sphere","authors":"C. García-Azpeitia","doi":"10.3934/JGM.2019021","DOIUrl":"https://doi.org/10.3934/JGM.2019021","url":null,"abstract":"This paper gives an analysis of the movement of begin{document}$ n $end{document} vortices on the sphere. When the vortices have equal circulation, there is a polygonal solution that rotates uniformly around its center. The main result concerns the global existence of relative periodic solutions that emerge from this polygonal relative equilibrium. In addition, it is proved that the families of relative periodic solutions contain dense sets of choreographies.","PeriodicalId":49161,"journal":{"name":"Journal of Geometric Mechanics","volume":"29 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2019-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89539586","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
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