{"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}
{"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}
{"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}
A. Dobrogowska, G. Jakimowicz, Karolina Wojciechowicz
{"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}
{"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}
{"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}
{"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}
{"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}
{"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}
{"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}