Journal of Geometry and Symmetry in Physics

Journal Information
ISSN / EISSN: 13125192 / 13145673
Total articles ≅ 122

Latest articles in this journal

Binuri Perera, Thanuja Paragoda, Dayal Dharmasena
Journal of Geometry and Symmetry in Physics, Volume 64; https://doi.org/10.7546/jgsp-64-2022-51-65

Abstract:
In this paper we survey Delaunay surfaces in $\mathbb{R}^{3}$ spanning two coaxial circles which appear as capillary surfaces supported on different solid supports in the absence of gravity. We classify these surfaces based on contact angles and the geometry of the support. Numerical solutions of the Euler Lagrange equation are provided using numerical methods.
Ying-Qiu Gu
Journal of Geometry and Symmetry in Physics, Volume 64; https://doi.org/10.7546/jgsp-64-2022-9-22

Abstract:
By means of hypercomplex numbers, in this paper we discuss algebraic equations and obtain some interesting relations. A structure equation $A^2=nA$ of a group is derived. The matrix representation of a group constitutes the basis elements of a hypercomplex number system. By a canonical real matrix representation of a cyclic group, we define the cyclic number system, which is exactly the solution space of the higher order algebraic equations, and thus can be used to solve the roots of algebraic equations. Hypercomplex numbers are linear algebras with definition of multiplication and division, satisfying the associativity and distributive law, which provide a unified, standard, and elegant language for many complex mathematical and physical objects. So, we have one more proof that the hypercomplex numbers are worthy of application in teaching and scientific research.
Taika Okuda, Akifumi Sako
Journal of Geometry and Symmetry in Physics, Volume 64; https://doi.org/10.7546/jgsp-64-2022-39-49

Abstract:
A construction methods of noncommutative locally symmetric K\"ahler manifolds via a deformation quantization with separation of variables was proposed by Sako-Suzuki-Umetsu and Hara-Sako. This construction gives the recurrence relations to determine the star product. These recurrence relations were solved for the case of the arbitrary one-dimensional ones, $N$-dimensional complex space, complex projective space and complex hyperbolic space. For any two-dimensional case, authors found the solution of the recurrence relations. In this paper, we review the solution and make the star product for two-dimensional complex projective space as a concrete example of this solution.
Clementina D. Mladenova,
Journal of Geometry and Symmetry in Physics, Volume 64; https://doi.org/10.7546/jgsp-64-2022-29-37

Abstract:
Dynamical orbits of the harmonic oscillator potential in the plane are ellipses which depend on a real parameter. Some time ago in this journal it has been proven by purely geometrical methods that the locus of the focuses of these ellipses are Cassinian ovals. Here we present several explicit analytic parameterizations of these remarkable curves. Nominally, their forms depend on the magnitude of the initial distance from the center of attraction and the magnitude of the initial velocity. We have found a few parameterizations in which the roles of the size and shapes can be clearly distinguished.
Detelina Kamburova, Rumen Marinov
Journal of Geometry and Symmetry in Physics, Volume 64; https://doi.org/10.7546/jgsp-64-2022-23-28

Abstract:
In this short note we present a new proof of Ekeland's variational principle and Caristi's fixed point theorem using a recently proved constrained variational principle in completely regular topological spaces.
Keiichi Kikuchi, Marin Drinov Academic Publishing House, Tsukasa Takeuchi
Journal of Geometry and Symmetry in Physics, Volume 63; https://doi.org/10.7546/jgsp-63-2022-39-64

Abstract:
Ikeda and Sakamoto studied a dynamical control problem called the linear first integral for holonomic dynamical systems, and our proposition proved the same result as theirs in integrability. % Also, a symplectic Haantjes manifolds has been defined by Tempesta and Tondo, which is a characterization of integrable systems using $(1,1)$ tensor fields. We show integrability in dynamical control problems from a geometric point of view by means of a concrete construction of a symplectic Haantjes manifold.
Ivaïlo M. Mladenov, Marin Drinov Academic Publishing House
Journal of Geometry and Symmetry in Physics, Volume 63; https://doi.org/10.7546/jgsp-63-2022-65-75

Abstract:
A plethora of explicit formulas that parameterize any type of the spiric sections are derived from the first principles.
Varun Jain, Rachna Rani, Rakesh Kumar
Journal of Geometry and Symmetry in Physics, Volume 63; https://doi.org/10.7546/jgsp-63-2022-21-37

Abstract:
We study generalized Cauchy-Riemann (GCR)-lightlike submanifolds of indefinite Kaehler manifolds admitting a quarter-symmetric non-metric connection. We derive a condition for a totally umbilical GCR-lightlike submanifold of indefinite Kaehler manifolds admitting a quarter-symmetric non-metric connection to be a totally geodesic submanifold. We study minimal GCR-lightlike submanifolds and obtain characterization theorem for a GCR-lightlike submanifold to be a GCR-lightlike product manifold.
Huchchappa A. Kumara, Marin Drinov Academic Publishing House, Venkatesha Venkatesha, Devaraja M. Naik
Journal of Geometry and Symmetry in Physics, Volume 61; https://doi.org/10.7546/jgsp-61-2021-41-51

Abstract:
In this work, we intend to investigate the characteristics of static perfect fluid space-time metrics on almost Kenmotsu manifolds. At first we prove that if a Kenmotsu manifold $M$ is the spatial factor of static perfect fluid space-time then it is $\eta$-Einstein. Moreover, if the Reeb vector field $\xi$ leaves the scalar curvature invariant, then $M$ is Einstein. Next we consider static perfect fluid space-time on almost Kenmotsu $(\kappa,\mu)'$-manifolds and give some characteristics under certain conditions.
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