Journal of Geometry and Symmetry in Physics

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ISSN / EISSN : 1312-5192 / 1314-5673
Total articles ≅ 116
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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.
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.
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.
Halima Loumi-Fergane, Marin Drinov Academic Publishing House
Journal of Geometry and Symmetry in Physics, Volume 61; https://doi.org/10.7546/jgsp-61-2021-53-78

Abstract:
Elsewhere, we gave the explicit expressions of the multivectors fields associated to infinitesimal symmetries which gave rise to Noether currents for classical field theories and relativistic mechanic using the Second Order Partial Differential Equation SOPDE condition for the Poincar\'e-Cartan form.\\ The main objective of this paper is to reformulate the multivector fields associated to translational and rotational symmetries of the gauge fields in particular those of the electromagnetic field which gave rise to symmetrical and invariant gauge energy-momentum tensor and the orbital angular momentum. The spin angular momentum appears however because of the internal symmetry inside the fiber.
Tuyen Nguyen, Marin Drinov Academic Publishing House, Vu Le
Journal of Geometry and Symmetry in Physics, Volume 61; https://doi.org/10.7546/jgsp-61-2021-79-104

Abstract:
In this paper, we consider exponential, connected and simply connected Lie groups which are corresponding to seven-dimensional Lie algebras such that their nilradical is a five-dimensional nilpotent Lie algebra $\mathfrak{g}_{5,2}$ given in Table~\ref{tab1}. In particular, we give a description of the geometry of the generic orbits in the coadjoint representation of some considered Lie groups. We prove that, for each considered group, the family of the generic coadjoint orbits forms a measurable foliation in the sense of Connes. The topological classification of these foliations is also provided.
Daniele Corradetti, Marin Drinov Academic Publishing House
Journal of Geometry and Symmetry in Physics, Volume 61; https://doi.org/10.7546/jgsp-61-2021-1-16

Abstract:
Recent papers contributed revitalizing the study of the exceptional Jordan algebra $\mathfrak{h}_{3}(\mathbb{O})$ in its relations with the true Standard Model gauge group $\mathrm{G}_{SM}$. The absence of complex representations of $\mathrm{F}_{4}$ does not allow $\Aut\left(\mathfrak{h}_{3}(\mathbb{O})\right)$ to be a candidate for any Grand Unified Theories, but the automorphisms of the complexification of this algebra, i.e., $\mathfrak{h}_{3}^{\mathbb{C}}(\mathbb{O})$, are isomorphic to the compact form of $\mathrm{E}_{6}$ and similar constructions lead to the gauge group of the minimal left-right symmetric extension of the Standard Model.
Mikhail V. Kharinov, Marin Drinov Academic Publishing House
Journal of Geometry and Symmetry in Physics, Volume 61; https://doi.org/10.7546/jgsp-61-2021-17-40

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.
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.
Cássio Murakami, Marin Drinov Academic Publishing House
Journal of Geometry and Symmetry in Physics, Volume 60; https://doi.org/10.7546/jgsp-60-2021-25-46

Abstract:
In the present article, an analysis was performed on the torque-free motion of a rigid body, developing Euler's analytical solution and Poinsot's geometric solution. The analytical solution for the angular velocity and Euler's angles was described given some initial conditions. Besides, an animation of Poinsot's geometric solution was elaborated and a study was carried out on the conditions in which the herpolhode forms a closed curve. Finally, an algorithm was developed that displays the obtained solutions, which also generates an animation of the geometric solution, and moreover provides an algorithm that produces closed herpolhodes.
Halil Yoldas, Marin Drinov Academic Publishing House
Journal of Geometry and Symmetry in Physics, Volume 60; https://doi.org/10.7546/jgsp-60-2021-83-94

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.
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