Pub Date : 2019-01-01DOI: 10.7546/jgsp-51-2019-29-39
A. Narmanov, E. Rajabov
{"title":"On the Geometry of Orbits of Conformal Vector Fields","authors":"A. Narmanov, E. Rajabov","doi":"10.7546/jgsp-51-2019-29-39","DOIUrl":"https://doi.org/10.7546/jgsp-51-2019-29-39","url":null,"abstract":"","PeriodicalId":43078,"journal":{"name":"Journal of Geometry and Symmetry in Physics","volume":"1 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71196014","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}
Pub Date : 2019-01-01DOI: 10.7546/jgsp-54-2019-1-12
N. Gürbüz, D. Yoon
A relativistic observer ξ needs reference frames in order to measure the movement and position of a object. If ξ is free falling, its restspaces are transported with LeviCivita parallelism. For accelerated observes, the restspaces are not transported by the Levi-Civita parallelism. In this case Fermi-Walker parallelism is used to define constant directions. Fermi-Walker parallelism is an isometry between the tangent spaces along relativistic observer ξ. [6, 11]. Balakrishnan et al investigated time evolutions of the space curve associated with a geometric phase using Fermi-Walker parallel transport in three dimensional Euclidean space [2]. Gürbüz had introduced new geometric phases according three classes of a curve evolution in Minkowski space [7, 8]. Usual Fermi-Walker parallel derivative for any vector field A is given with respect to Frenet frame {t, n, b} in three dimensional Euclidean space as following (cf. [9]) DfA Dfs = dA
一个相对论观察者ξ需要参考系来测量一个物体的运动和位置。如果ξ是自由落体的，则其剩余空间以列维维塔平行度传输。对于加速观测，静止空间不受列维-奇维塔平行度的传输。在这种情况下，费米-沃克平行度被用来定义恒定方向。费米-沃克平行度是沿相对论观察者ξ的切空间之间的等距。(6, 11)。Balakrishnan等人利用三维欧几里得空间[2]中的费米-沃克平行输运研究了与几何相位相关的空间曲线的时间演化。g rb z根据Minkowski空间中曲线演化的三类引入了新的几何相[7,8]。通常在三维欧几里德空间中，任意向量场A对Frenet坐标系{t, n, b}的费米-沃克平行导数如下(cf. [9]) DfA Dfs = dA
{"title":"Fermi-Walker Parallel Transport According to Quasi Frame in Three Dimensional Minkowski Space","authors":"N. Gürbüz, D. Yoon","doi":"10.7546/jgsp-54-2019-1-12","DOIUrl":"https://doi.org/10.7546/jgsp-54-2019-1-12","url":null,"abstract":"A relativistic observer ξ needs reference frames in order to measure the movement and position of a object. If ξ is free falling, its restspaces are transported with LeviCivita parallelism. For accelerated observes, the restspaces are not transported by the Levi-Civita parallelism. In this case Fermi-Walker parallelism is used to define constant directions. Fermi-Walker parallelism is an isometry between the tangent spaces along relativistic observer ξ. [6, 11]. Balakrishnan et al investigated time evolutions of the space curve associated with a geometric phase using Fermi-Walker parallel transport in three dimensional Euclidean space [2]. Gürbüz had introduced new geometric phases according three classes of a curve evolution in Minkowski space [7, 8]. Usual Fermi-Walker parallel derivative for any vector field A is given with respect to Frenet frame {t, n, b} in three dimensional Euclidean space as following (cf. [9]) DfA Dfs = dA","PeriodicalId":43078,"journal":{"name":"Journal of Geometry and Symmetry in Physics","volume":"1 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71196444","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}
Pub Date : 2019-01-01DOI: 10.7546/JGSP-52-2019-1-15
N. Ausheva, V. Olevskyi, Yu. B. Olevska
A method is proposed for constructing minimal surfaces based on fifth-order Bezier isotropic curves specified in a vector-parametric form, allowing control of the guide curve and the surface in user mode. The coefficients of the basic quadratic forms were calculated and it was shown that the surfaces would be minimal. An example of a surface constructed by the proposed method is given.
{"title":"Modeling of Minimal Surface Based on an Isotropic Bezier Curve of Fifth Order","authors":"N. Ausheva, V. Olevskyi, Yu. B. Olevska","doi":"10.7546/JGSP-52-2019-1-15","DOIUrl":"https://doi.org/10.7546/JGSP-52-2019-1-15","url":null,"abstract":"A method is proposed for constructing minimal surfaces based on fifth-order Bezier isotropic curves specified in a vector-parametric form, allowing control of the guide curve and the surface in user mode. The coefficients of the basic quadratic forms were calculated and it was shown that the surfaces would be minimal. An example of a surface constructed by the proposed method is given.","PeriodicalId":43078,"journal":{"name":"Journal of Geometry and Symmetry in Physics","volume":"1 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71196845","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}
Pub Date : 2019-01-01DOI: 10.7546/jgsp-52-2019-47-66
A. Dobrogowska, G. Jakimowicz, Karolina Wojciechowicz
Communicated by Alexandar B. Yanovski Abstract. In the case when M is equipped with a bi-Hamiltonian structure (M,π1, π2) we show how to construct family of Poisson structures on the tangent bundle TM to a Poisson manifold. Moreover we present how to find Casimir functions for those structures and we discuss some particular examples. MSC : 53D17, 37K10
{"title":"Bi-Hamiltonian Structures on the Tangent Bundle to a Poisson Manifold","authors":"A. Dobrogowska, G. Jakimowicz, Karolina Wojciechowicz","doi":"10.7546/jgsp-52-2019-47-66","DOIUrl":"https://doi.org/10.7546/jgsp-52-2019-47-66","url":null,"abstract":"Communicated by Alexandar B. Yanovski Abstract. In the case when M is equipped with a bi-Hamiltonian structure (M,π1, π2) we show how to construct family of Poisson structures on the tangent bundle TM to a Poisson manifold. Moreover we present how to find Casimir functions for those structures and we discuss some particular examples. MSC : 53D17, 37K10","PeriodicalId":43078,"journal":{"name":"Journal of Geometry and Symmetry in Physics","volume":"1 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71196503","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}
Pub Date : 2019-01-01DOI: 10.7546/jgsp-53-2019-85-102
A. Sasane, V. Ufnarovski
{"title":"Eigenvectors of the SO(3,${mathbb{R}}$) Matrices","authors":"A. Sasane, V. Ufnarovski","doi":"10.7546/jgsp-53-2019-85-102","DOIUrl":"https://doi.org/10.7546/jgsp-53-2019-85-102","url":null,"abstract":"","PeriodicalId":43078,"journal":{"name":"Journal of Geometry and Symmetry in Physics","volume":"1 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71196847","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}
Pub Date : 2019-01-01DOI: 10.7546/jgsp-53-2019-1-19
L. Belarbi, H. Elhendi
{"title":"Geometry of Twisted Sasaki Metric","authors":"L. Belarbi, H. Elhendi","doi":"10.7546/jgsp-53-2019-1-19","DOIUrl":"https://doi.org/10.7546/jgsp-53-2019-1-19","url":null,"abstract":"","PeriodicalId":43078,"journal":{"name":"Journal of Geometry and Symmetry in Physics","volume":"1 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71196887","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}
Pub Date : 2019-01-01DOI: 10.7546/jgsp-52-2019-17-26
A. Blaga
{"title":"Some Geometrical Aspects of Einstein, Ricci and Yamabe Solitons","authors":"A. Blaga","doi":"10.7546/jgsp-52-2019-17-26","DOIUrl":"https://doi.org/10.7546/jgsp-52-2019-17-26","url":null,"abstract":"","PeriodicalId":43078,"journal":{"name":"Journal of Geometry and Symmetry in Physics","volume":"1 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71196482","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}
Pub Date : 2019-01-01DOI: 10.7546/jgsp-51-2019-87-102
A. Viña
{"title":"Charge of D-Branes","authors":"A. Viña","doi":"10.7546/jgsp-51-2019-87-102","DOIUrl":"https://doi.org/10.7546/jgsp-51-2019-87-102","url":null,"abstract":"","PeriodicalId":43078,"journal":{"name":"Journal of Geometry and Symmetry in Physics","volume":"1 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71196218","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}
Pub Date : 2019-01-01DOI: 10.7546/JGSP-51-2019-9-28
D. Grantcharov, G. Grantcharov
Communicated by Ivaïlo M. Mladenov Abstract. We consider a modified Kostant-Souriau geometric quantization scheme due to Czyz and Hess for Hamiltonian systems on the cotangent bundles of compact rank-one Riemannian symmetric spaces (CROSS). It is used, together with a symplectic reduction process, to relate its energy spectrum to the spectrum of the Laplace-Beltrami operator. Moreover, the corresponding eigenspaces have real dimension equal to the complex dimension of the space of the holomorphic sections of the quantum bundle which is obtained after the quantization. The relation between the two constructions was first noticed by Mladenov and Tsanov for the case of the spheres. In addition to the CROSS case, we announce preliminary results related to the case of compact Riemannian symmetric spaces of higher rank.
由Ivaïlo M. Mladenov传达摘要。考虑紧致列- 1黎曼对称空间(CROSS)的协切束上哈密顿系统的一种基于Czyz和Hess的改进Kostant-Souriau几何量化方案。它与辛约简过程一起使用，将其能谱与拉普拉斯-贝尔特拉米算子的能谱联系起来。相应的本征空间的实维数等于量子化后得到的量子束全纯截面空间的复维数。这两种结构之间的关系首先是由Mladenov和Tsanov在球体的情况下注意到的。除了交叉情况外，我们还公布了有关高秩紧黎曼对称空间情况的初步结果。
{"title":"Relations Between Laplace Spectra and Geometric Quantization of Reimannian Symmetric Spaces","authors":"D. Grantcharov, G. Grantcharov","doi":"10.7546/JGSP-51-2019-9-28","DOIUrl":"https://doi.org/10.7546/JGSP-51-2019-9-28","url":null,"abstract":"Communicated by Ivaïlo M. Mladenov Abstract. We consider a modified Kostant-Souriau geometric quantization scheme due to Czyz and Hess for Hamiltonian systems on the cotangent bundles of compact rank-one Riemannian symmetric spaces (CROSS). It is used, together with a symplectic reduction process, to relate its energy spectrum to the spectrum of the Laplace-Beltrami operator. Moreover, the corresponding eigenspaces have real dimension equal to the complex dimension of the space of the holomorphic sections of the quantum bundle which is obtained after the quantization. The relation between the two constructions was first noticed by Mladenov and Tsanov for the case of the spheres. In addition to the CROSS case, we announce preliminary results related to the case of compact Riemannian symmetric spaces of higher rank.","PeriodicalId":43078,"journal":{"name":"Journal of Geometry and Symmetry in Physics","volume":"1 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71196335","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}
Pub Date : 2019-01-01DOI: 10.7546/jgsp-54-2019-37-54
L. B. Natividad, Job A. Nable
{"title":"Wigner Functions and Weyl Operators on the Euclidean Motion Group","authors":"L. B. Natividad, Job A. Nable","doi":"10.7546/jgsp-54-2019-37-54","DOIUrl":"https://doi.org/10.7546/jgsp-54-2019-37-54","url":null,"abstract":"","PeriodicalId":43078,"journal":{"name":"Journal of Geometry and Symmetry in Physics","volume":"1 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71196519","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}
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