International Journal of Geometric Methods in Modern Physics

We study complete linear Weingarten spacelike submanifolds with arbitrary high codimension $p$ in the de Sitter space ${𝕊}_p^{n+p}$ of index $p$ and whose normalized mean curvature vector is parallel. Under suitable restrictions on the values of the mean curvature function and on the norm of the traceless part of the second fundamental form, we prove that such a spacelike submanifold must be either totally umbilical or isometric to a certain hyperbolic cylinder of ${𝕊}_p^{n+p}$. Our approach is based on the use of a Simons type formula related to an appropriate Cheng–Yau modified operator jointly with an extension of Hopf’s maximum principle for complete Riemannian manifolds.

Recently, the quantum spectrum of black BIons has been considered and their entropies have been calculated. Generalizing this model to a tube of water which interacts with DNA waves, its quantum spectrum and entropy could be obtained. A DNA can emit two types of waves, including electromagnetic waves (EMS) and topoisomerase-like ones. EMS carry messages of a DNA and help it to communicate with other DNAs and also pure water. Topoisomerase-like waves open packings of a DNA and copy its genetic information. Both of these waves could interact with pure water and change its entropy and quantum spectrum.

We apply the central extension technique of Poincaré to dynamics involving an interacting mixture of pressureless matter and vacuum near a finite-time singularity. We show that the only attractor solution on the circle of infinity is the one describing a vanishing matter-vacuum model at early times.

In this paper, we use less topological restrictions and more geometric and analytic conditions to obtain some sufficient conditions on Yamabe solitons such that their metrics are Yamabe metrics, that is, metrics of constant scalar curvature. More precisely, we use properties of conformal vector fields to find several sufficient conditions on the soliton vector fields of Yamabe solitons under which their metrics are Yamabe metrics.

In this paper, we find solutions for the Klein–Gordon equation in the presence of a Cornell potential under the influence of noninertial effects in the cosmic string space-time. Then, we study Klein–Gordon oscillator in the cosmic string space-time. In addition, we show that the presence of a Cornell potential causes the forming bound states for the Klein–Gordon equation in this kind of background.

We analyze the Casalbuoni–Brink–Schwarz superparticle model on a 2-dimensional curved spacetime as a super Finsler metric defined on a (2,2)-dimensional supermanifold. We propose a nonlinear Finsler connection which preserves this Finsler metric and calculates it explicitly. The equations of motion of the superparticle are reconstructed in the form of auto-parallel equations expressed by the super nonlinear connection.

In this paper, we have investigated the stability of a spherically symmetric object with charged anisotropic matter by using the concept of cracking. The cracking is a very intuitive technique to check the stability which is based on the analysis of the radial forces that appear on the system due to perturbations taking it out of its equilibrium state. For this, we have applied and studied the effect of local density perturbations to the hydrostatic equilibrium equation and on all the physical parameters with generalized polytropic equation of state. It is found that some of the generalized polytropic models exhibit cracking.

The Newton–Cartan theory of gravity is expressed in the language of $D$-differentiation. A characteristic of this approach is that the same framework accommodates, together with classical gravity, also non-relativistic Quantum Mechanics (coupled to gravity), both in its standard Schrödingerian form and in that of de Broglie and Bohm.

With the extended navigation data, we consider the generalized Zermelo navigation on Riemannian manifolds, admitting a space-dependent ship’s speed in the presence of perturbation determined by a weak velocity vector field, with application of Finsler metric of Randers type. The approach is shown via indicatrix and inner product. We also compare our findings in the context of conformality for the cases of weak and critical winds. The study is illustrated with the example in dimension 2.

The aim of this paper is to investigate a generalized Rikitake system from the integrability point of view. For the integrable case, we derive a family of integrable deformations of the generalized Rikitake system by altering its constants of motion, and give two classes of Hamilton–Poisson structures which implies these integrable deformations, including the generalized Rikitake system, are bi-Hamiltonian and have infinitely many Hamilton–Poisson realizations. By analyzing properties of the differential Galois groups of normal variational equations (NVEs) along certain particular solution, we show that the generalized Rikitake system is not rationally integrable in an extended Liouville sense for almost all parameter values, which is in accord with the fact that this system admits chaotic behaviors for a large range of its parameters. The non-existence of analytic first integrals are also discussed.

The objective of this study is to define an ovaloid surface on the convex closed space-like surfaces of constant breadth when principal curvatures of these surfaces are continuous, non-vanishing functions, and to obtain some special geometrical properties of this ovaloid surface by using the radius of curvature, diameter of the surface in $E_1^3$.

The Ricci tensor of a Robertson–Walker (RW) space-time is here specified by requiring constancy of the scalar curvature and a vanishing spatial curvature. By entering this Ricci tensor in Einstein’s equations (without cosmological constant), the cosmological fluid shows a transition from a pure radiation to a Lambda equation of state. In other words, the RW geometry with constant scalar curvature and flat space fixes the limit values $w=1/3$ and $w=-1$, without any hypothesis on the cosmological fluid. The value of the scalar curvature fixes the time-scale for the transition.

For this reason, we investigate the ‘toy-universe’ with Hubble parameter $h=0.673$ and temperature $T_{\mathrm{\text{CMB}}}=2.72$K. The model predicts an age of the universe in the range 7.3–13.7Gyr.

Let $(M,g)$ be a pseudo-Riemannian manifold and $T^{2}M$ be its second-order tangent bundle equipped with the deformed $2$nd lift metric $\overline{g}$ which is obtained from the $2$nd lift metric by deforming the horizontal part with a symmetric $(0,2)$-tensor field $c$. In the present paper, we first compute the Levi-Civita connection and its Riemannian curvature tensor field of $(T^{2}M,\overline{g})$. We give necessary and sufficient conditions for $(T^{2}M,\overline{g})$ to be semi-symmetric. Secondly, we show that $(T^{2}M,\overline{g})$ is a plural-holomorphic $B$-manifold with the natural integrable nilpotent structure. Finally, we get the conditions under which $(T^{2}M,\overline{g})$ with the $2$nd lift of an almost complex structure is an anti-Kähler manifold.

We applied the theory of regularly varying (RV) functions to the analysis of the cosmological parameters for the $\mathrm{\Lambda }$CDM model with the matter-dominated evolution. Carroll et al. proved in 1992 that for this type of universe with the curvature $k=0,-1$, the expression $H(t)t$ ($H(t)$ is the Hubble parameter) depends solely on the density parameter $\mathrm{\Omega }(t)$. Using this result, we infer for such universe the complete asymptotics of all main cosmological parameters. More specifically, the following is derived. If the limit $\omega ={lim}_{t\to \infty }\mathrm{\Omega }(t)$ does exist and $\omega \ne 0$, then the cosmological constant $\mathrm{\Lambda }$ is equal to $0$. If $\omega =0$, then for the expansion scale factor $a(t)$ of a flat universe, we have $a(t)\sim e^{\sqrt{\mathrm{\Lambda }/3}t}$. On the other hand, if the limit ${lim}_{t\to \infty }\mathrm{\Omega }(t)$ does not exist, then $a(t)$ bounces between two power functions and therefore has infinitely many flexion points. Hence, the deceleration parameter in this case changes the sign infinitely many times.

The magnetosphere structure of compact objects is considered in the context of a theory of gravity with dynamical torsion field beyond standard General Relativity (GR). To this end, a new spherically symmetric solution is obtained in this theoretical framework, physically representing a compact object of pseudoscalar fields (for example, axion field). The axially symmetric version of the Grad–Shafranov equation (GSE) is also derived in this context, and used to describe the magnetosphere dynamics of the obtained “axion star”. The interplay between high-energy processes and the seed magnetic field with respect to the global structure of the magnetosphere is briefly discussed.

In the recent decade, many investigations have been done in the framework of generalized uncertainty principle (GUP), but the phenomenology of models in this framework are less studied. In this work, the applications of Biot–Savart law in the presence of a minimal length scale are investigated. We obtain the modified magnetostatic field from an infinitely long, straight wire carrying current $I$. Also, the modified magnetostatic field from a circular loop carrying current $I$ and the modified magnetostatic field of an ideal solenoid are found. It is interesting to note that in the limit $a=\hslash \sqrt{2\beta }\to 0$, all of the modified magnetostatic fields become their usual forms.

Here in this work, we investigated the possible cosmological consequences of the interaction of Brans–Dicke scalar field and massive scalar field by considering spherically symmetric Robertson–Walker metric. The present problem can also be treated as an extension work of [K. Priyokumar et al., Interaction of gravitational field and Brans–Dicke field, Res. Astron. Astrophys. 16(4) (2016) 64; K. Priyokumar and M. Dewri, Interaction of electromagnetic field and Brans–Dicke field, Chinease J. Phys. 54 (2016) 845]. The exact solutions of the field equations are obtained with seven different cases. The behavior of the model and their contribution to the process of the evolution are examined in detail from some explicit and reasonable values of free parameter. We also presented the variations of certain physical parameters versus cosmic time graphically to compare our solutions with the present observational findings. When we studied further, it is found that the cosmological term $\mathrm{\Lambda }$ takes a great role in the accelerating expansion of our universe when both scalar fields are exponentially increasing functions of time, while the cosmological term will not appear in the case when both the scalar fields are exponentially decreasing functions of time. Also, the scalar field is seen to have a tendency to increase the expansion of the universe, thereby flattening the universe.