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Journal of Geometry and Symmetry in Physics最新文献

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Permutable Symmetric Hadamard Matrices in Quaternion Algebra and Engineering Applications 四元数代数中的置换对称Hadamard矩阵及其工程应用
IF 0.4
Journal of Geometry and Symmetry in Physics Pub Date : 2021-11-30 DOI: 10.7546/jgsp-61-2021-17-40
M. Kharinov
{"title":"Permutable Symmetric Hadamard Matrices in Quaternion Algebra and Engineering Applications","authors":"M. Kharinov","doi":"10.7546/jgsp-61-2021-17-40","DOIUrl":"https://doi.org/10.7546/jgsp-61-2021-17-40","url":null,"abstract":"In this paper, aiming to develop the group and out-of-group formalization of the symmetry concept, the preservation of a matrix symmetry after row permutation is considered by the example of the maximally permutable emph{normalized} Hadamard matrices which row and column elements are either plus or minus one. These matrices are used to extend the additive decomposition of a linear operator into symmetric and skew-symmetric parts using several commuting operations of the Hermitian conjugation type, for the quaternionic generalization of a vector cross product, as well as for creating educational puzzles and other applications.","PeriodicalId":43078,"journal":{"name":"Journal of Geometry and Symmetry in Physics","volume":"1 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2021-11-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44482826","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Gauss Maps of the Surfaces in the Three-Dimensional Heisenberg Group 三维海森堡群表面的高斯映射
IF 0.4
Journal of Geometry and Symmetry in Physics Pub Date : 2021-07-01 DOI: 10.7546/jgsp-60-2021-1-23
Christiam Figueroa
{"title":"Gauss Maps of the Surfaces in the Three-Dimensional Heisenberg Group","authors":"Christiam Figueroa","doi":"10.7546/jgsp-60-2021-1-23","DOIUrl":"https://doi.org/10.7546/jgsp-60-2021-1-23","url":null,"abstract":"In this paper we study the Gauss map of surfaces in three-dimensional Heisenberg group using the Gans model of the hyperbolic plane. We establish a relationship between the tension fields of the Gauss maps and the mean curvatures of the surfaces in $mathcal{H}_{3}$.","PeriodicalId":43078,"journal":{"name":"Journal of Geometry and Symmetry in Physics","volume":"56 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2021-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77238897","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Primitive Tilings and Coherent Frames 原始平铺和相干帧
IF 0.4
Journal of Geometry and Symmetry in Physics Pub Date : 2021-07-01 DOI: 10.7546/jgsp-60-2021-47-64
L. Silvestre, E. Miro, Job A. Nable
{"title":"Primitive Tilings and Coherent Frames","authors":"L. Silvestre, E. Miro, Job A. Nable","doi":"10.7546/jgsp-60-2021-47-64","DOIUrl":"https://doi.org/10.7546/jgsp-60-2021-47-64","url":null,"abstract":"This paper characterizes primitive substitution tiling systems for Lie groups for which every element of the associated tiling space generates coherent frames for corresponding representation spaces.","PeriodicalId":43078,"journal":{"name":"Journal of Geometry and Symmetry in Physics","volume":" ","pages":""},"PeriodicalIF":0.4,"publicationDate":"2021-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47705280","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
New Parameterizations of (mathrm{SL}(2,mathbb{R})) and Some Explicit Formulas for Its Logarithm (mathrm{SL}(2,mathbb{R}))的新参数化及其对数的若干显式公式
IF 0.4
Journal of Geometry and Symmetry in Physics Pub Date : 2021-07-01 DOI: 10.7546/jgsp-60-2021-65-81
T. Valchev, C. Mladenova, I. Mladenov
{"title":"New Parameterizations of (mathrm{SL}(2,mathbb{R})) and Some Explicit Formulas for Its Logarithm","authors":"T. Valchev, C. Mladenova, I. Mladenov","doi":"10.7546/jgsp-60-2021-65-81","DOIUrl":"https://doi.org/10.7546/jgsp-60-2021-65-81","url":null,"abstract":"Here we demonstrate some of the benefits of a novel parameterization of the Lie groups $mathrm{Sp}(2,bbr)congmathrm{SL}(2,bbr)$. Relying on the properties of the exponential map $mathfrak{sl}(2,bbr)tomathrm{SL}(2,bbr)$, we have found a few explicit formulas for the logarithm of the matrices in these groups. Additionally, the explicit analytic description of the ellipse representing their field of values is derived and this allows a direct graphical identification of various types.","PeriodicalId":43078,"journal":{"name":"Journal of Geometry and Symmetry in Physics","volume":" ","pages":""},"PeriodicalIF":0.4,"publicationDate":"2021-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47424255","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Some Results on Cosymplectic Manifolds Admitting Certain Vector Fields 关于允许某些向量场的辛流形的一些结果
IF 0.4
Journal of Geometry and Symmetry in Physics Pub Date : 2021-07-01 DOI: 10.7546/jgsp-60-2021-83-94
H. Yoldaş
{"title":"Some Results on Cosymplectic Manifolds Admitting Certain Vector Fields","authors":"H. Yoldaş","doi":"10.7546/jgsp-60-2021-83-94","DOIUrl":"https://doi.org/10.7546/jgsp-60-2021-83-94","url":null,"abstract":"The purpose of present paper is to study cosymplectic manifolds admitting certain special vector fields such as holomorphically planar conformal (in short HPC) vector field. First, we prove that an HPC vector field on a cosymplectic manifold is also a Jacobi-type vector field. Then, we obtain the necessary conditions for such a vector field to be Killing. Finally, we give an important characterization for a torse-forming vector field on such a manifold given as to be recurrent.","PeriodicalId":43078,"journal":{"name":"Journal of Geometry and Symmetry in Physics","volume":" ","pages":""},"PeriodicalIF":0.4,"publicationDate":"2021-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47769893","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Classically Integrable Non-Linear Sigma Models and their Geometric Properties 经典可积非线性模型及其几何性质
IF 0.4
Journal of Geometry and Symmetry in Physics Pub Date : 2021-01-01 DOI: 10.7546/JGSP-59-2021-47-65
P. Bracken
{"title":"Classically Integrable Non-Linear Sigma Models and their Geometric Properties","authors":"P. Bracken","doi":"10.7546/JGSP-59-2021-47-65","DOIUrl":"https://doi.org/10.7546/JGSP-59-2021-47-65","url":null,"abstract":"General classes of non-linear sigma models originating from a specified action are developed and studied. Models can be grouped and considered within a single mathematical structure this way. The geometrical properties of these models and the theories they describe are developed in detail. The zero curvature representation of the equations of motion are found. Those representations which have a spectral parameter are of importance here. Some new models with Lax pairs which depend on a spectral parameter are found. Some particular classes of solutions are worked out and discussed.","PeriodicalId":43078,"journal":{"name":"Journal of Geometry and Symmetry in Physics","volume":"37 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82238336","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Symbol Correspondence for Euclidean Systems 欧几里得系统的符号对应
IF 0.4
Journal of Geometry and Symmetry in Physics Pub Date : 2021-01-01 DOI: 10.7546/jgsp-62-2021-67-84
L. B. Natividad, Job A. Nable
{"title":"Symbol Correspondence for Euclidean Systems","authors":"L. B. Natividad, Job A. Nable","doi":"10.7546/jgsp-62-2021-67-84","DOIUrl":"https://doi.org/10.7546/jgsp-62-2021-67-84","url":null,"abstract":"The three main objects that serve as the foundation of quantum mechanics on phase space are the Weyl transform, the Wigner distribution function, and the $star$-product of phase space functions. In this article, the $star$-product of functions on the Euclidean motion group of rank three, $mathrm{E}(3)$, is constructed. $C^*$-algebra properties of $star_s$ on $mathrm{E}(3)$ are presented, establishing a phase space symbol calculus for functions whose parameters are translations and rotations. The key ingredients in the construction are the unitary irreducible representations of the group.","PeriodicalId":43078,"journal":{"name":"Journal of Geometry and Symmetry in Physics","volume":"1 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71196975","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A Note on the Representation of Clifford Algebras 关于Clifford代数表示的注解
IF 0.4
Journal of Geometry and Symmetry in Physics Pub Date : 2021-01-01 DOI: 10.7546/jgsp-62-2021-29-52
Ying-Qiu Gu
{"title":"A Note on the Representation of Clifford Algebras","authors":"Ying-Qiu Gu","doi":"10.7546/jgsp-62-2021-29-52","DOIUrl":"https://doi.org/10.7546/jgsp-62-2021-29-52","url":null,"abstract":"In this note we construct explicit complex and real faithful matrix representations of the Clifford algebras $Cl_{p,q}$. The representation is based on Pauli matrices and has an elegant structure similar to the fractal geometry. In the cases $p+q=4m$, the representation is unique in equivalent sense, and the $1+3$ dimensional space-time corresponds to the simplest and best case. Besides, the relation between the curvilinear coordinate frame and the local orthonormal basis in the curved space-time is discussed in detail, the covariant derivatives of the spinor and tensors are derived, and the connection of the orthogonal basis in tangent space is calculated. These results are helpful for both theoretical analysis and practical calculation. The basis matrices are the faithful representation of Clifford algebras in any $p+q$ dimensional Minkowski space-time or Riemann space, and the Clifford calculus converts the complicated relations in geometry and physics into simple and concise algebraic operations. Clifford numbers over any number field $mathbb{F}$ expressed by this matrix basis form a well-defined $2^n$ dimensional hypercomplex number system. Therefore, we can expect that Clifford algebras will complete a large synthesis in science.","PeriodicalId":43078,"journal":{"name":"Journal of Geometry and Symmetry in Physics","volume":"1 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71197101","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 4
Twisted Sasakian Metric on the Tangent Bundle and Harmonicity 切线束上的扭曲sasaki度量与调和性
IF 0.4
Journal of Geometry and Symmetry in Physics Pub Date : 2021-01-01 DOI: 10.7546/jgsp-62-2021-53-66
F. Latti, H. Elhendi, L. Belarbi
{"title":"Twisted Sasakian Metric on the Tangent Bundle and Harmonicity","authors":"F. Latti, H. Elhendi, L. Belarbi","doi":"10.7546/jgsp-62-2021-53-66","DOIUrl":"https://doi.org/10.7546/jgsp-62-2021-53-66","url":null,"abstract":"In the present paper, we introduce a new class of natural metrics on the tangent bundle $TM$ of the Riemannian manifold $(M,g)$ denoted by $G^{f,h}$ which is named a twisted Sasakian metric. A necessary and sufficient conditions under which a vector field is harmonic with respect to the twisted Sasakian metric are established. Some examples of harmonic vector fields are presented as well.","PeriodicalId":43078,"journal":{"name":"Journal of Geometry and Symmetry in Physics","volume":"1 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71197323","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Remarks on Riemann and Ricci Solitons in $(alpha,beta)$-Contact Metric Manifolds 关于$(alpha,beta)$ -接触度量流形中的Riemann和Ricci孤子的注解
IF 0.4
Journal of Geometry and Symmetry in Physics Pub Date : 2020-09-05 DOI: 10.7546/JGSP-58-2020-1-12
A. Blaga, D. Laţcu
{"title":"Remarks on Riemann and Ricci Solitons in $(alpha,beta)$-Contact Metric Manifolds","authors":"A. Blaga, D. Laţcu","doi":"10.7546/JGSP-58-2020-1-12","DOIUrl":"https://doi.org/10.7546/JGSP-58-2020-1-12","url":null,"abstract":"We study almost Riemann solitons and almost Ricci solitons in an $(alpha,beta)$-contact metric manifold satisfying some Ricci symmetry conditions, treating the case when the potential vector field of the soliton is pointwise collinear with the structure vector field.","PeriodicalId":43078,"journal":{"name":"Journal of Geometry and Symmetry in Physics","volume":"1 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2020-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42151573","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","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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