International Journal of Geometric Methods in Modern Physics

In this paper, we classify all simply connected five-dimensional nilpotent Lie groups which admit $(\alpha ,\beta )$-metrics of Berwald and Douglas type defined by a left invariant Riemannian metric and a left invariant vector field. During this classification, we give the geodesic vectors, Levi-Civita connection, curvature tensor, sectional curvature and $S$-curvature.

In this paper, Bianchi type I space-times in the $f(R)$ theory of gravity are classified via conformal vector fields using algebraic and direct integration techniques. In this classification, we show that the conformal vector fields are of dimension four, five, six or fifteen. Additionally, we found that non-conformally flat Bianchi type I space-times admit conformal vector fields of dimension four, five or six. In the case of conformally flat or flat space-times, the dimension of the conformal vector fields is fifteen.

We characterize the second variation of an higher order Lagrangian by a Jacobi morphism and by currents strictly related to the geometric structure of the variational problem. We discuss the relation between the Jacobi morphism and the Hessian at an arbitrary order. Furthermore, we prove that a pair of Jacobi fields always generates a (weakly) conserved current. An explicit example is provided for a Yang–Mills theory on a Minkowskian background.

We investigate the chameleon Brans–Dicke gravity with new holographic dark energy which includes a non-minimal coupling between matter and scalar field. We use parameterized forms of deceleration parameter for flat FRW universe, which play a vital role to describe the nature of cosmic acceleration. We explore the cosmological parameters like Hubble parameter, equation of state parameter as well as its plane and stability of the obtained solution. The results of cosmological parameter and plane are consistent with observational data.

Rip cosmological models have been investigated in the framework of $f(T,{𝒯})$ theory of gravity, where $T$ denotes the torsion and ${𝒯}$ is the trace of the energy–momentum tensor. These phantom cosmological models revealed that at initial epoch a EoS parameter $\omega <-1$ tends asymptotically at late phase to $-1$ $(\omega \to -1)$. On the other hand, Wormhole Solutions and Big Trip have been subject to an investigation. The wormhole throat radius $R(t)$ and the conditions to be satisfied to produce the Big Trip phenomenon have been discussed.

In this paper, we study naturally reductive $(\alpha ,\beta )$-metrics on homogeneous manifolds. We show that naturally reductive $(\alpha ,\beta )$-metrics arise only when $\alpha$ is naturally reductive and some conditions on $\varphi$ is satisfied. We give an explicit formula for the flag curvature of naturally reductive $(\alpha ,\beta )-$metrics which improves the flag curvature formula of naturally reductive Randers metrics given in [D. Latifi, Naturally reductive homogeneous Randers spaces, J. Geom. Phys. 60 (2010) 1968–1973]. As a special case, we give an explicit formula for the flag curvature of bi-invariant $(\alpha ,\beta )$-metrics on Lie groups.

The focus of this paper is on Kawahara equation (KE) which models diverse variety of waves enforced in many branches of applied sciences. Symmetries to the considered equation are successfully obtained by practicing nonclassical method. According to nonclassical symmetries, KE has been reduced to numerous ODEs. Further, these ODEs are treated such that new analytic solutions are determined by applying power series, ansätz and $(\frac{G^{\prime }}{G^2})$-expansion method.

We geometrically examine the entanglement in symmetric multiquibt states using the spin coherent states properties. We employ the Majorana representation to examine how coherent (polarized) and unpolarized states can be represented in the Bloch sphere and subsequently to quantify entanglement in multipartite systems. Entanglement can be viewed as a distance separate two points in Bloch sphere and how this notion can be extended for multipartite states in W class. This provides us with an entanglement measure for $W$-states analogue to the notion of Concurrence.

Assuming the most general form of static spherically symmetric space-times, we search for the conformal vector fields in $f(R,G)$ gravity by means of algebraic and direct integration approaches. In this study, there exist six cases which on account of further study yield conformal vector fields of dimension four, six and fifteen. During this study, we also recovered some well-known static spherically symmetric metrics announced in the current literature.

In this work, several pinched conditions on the Laplacian and gradient of the warping function are found in consideration of warped product submanifolds structure that force to homology groups vanish with no stable currents. Also, it is proved that a warped product pointwise semi-slant submanifold $M^n$ that is compact and oriented in an odd-dimensional spheres ${𝕊}^{2(\frac{p}{2}+q)+1}$ and ${𝕊}^{2(p+q)+1}$, has no stable integral $p+1$-currents and $2p+1$-currents, respectively, and their homology groups are null, provided squared norm of the gradient for warping function satisfies some extrinsic restrictions including the Laplacian of the warping function, pointwise slant functions in addition to dimension of fiber of warped product immersions. Moreover, under assumption of extrinsic condition on the warping function, it is show $M^n$ being homeomorphic to a standard sphere ${𝕊}^n$ with $n=4$ and homotopic to a standard sphere ${𝕊}^n$ with $n=3$. Further, the same results are generalized for contact CR-warped product submanifolds of same ambient spaces.

We show how to lift a Riemannian metric and almost symplectic form on a manifold to a Riemannian structure on a canonically associated supermanifold known as the antitangent or shifted tangent bundle. We view this construction as a generalization of Sasaki’s construction of a Riemannian metric on the tangent bundle of a Riemannian manifold.

The propagation of cylindrical shock wave under the influence of axial magnetic field in rotating medium under isothermal flow condition is investigated. The density, magnetic field and azimuthal and axial components of fluid velocity are assumed to be varying in the undisturbed medium. The arbitrary constants appearing in the expressions for infinitesimals of the Local Lie group of transformations bring about three different cases of solutions, i.e. with power law shock path, exponential law shock path and a particular case of power law shock path. Numerical solutions are obtained in the cases of power law and exponential law shock paths. Distribution of gasdynamical quantities are discussed through figures. The effects of variation in values of Alfven-Mach number $M_A^{-2}$, ambient azimuthal velocity index ${\lambda }_1$ and ambient density index $\varphi$ are studied on flow variables and on shock strength. The numerical integration is done using software Mathematica. It is obtained that magnetic field has a decaying effect on shock strength. Also, increase in value of ambient density or ambient azimuthal velocity variation index in the case of power law shock path and increase in value of ambient density variation index in case of exponential law shock path have the decaying effect on shock strength.

In this paper, we studied the cosmological implications of generalized ghost Tsallis holographic dark energy in the framework of Randall–Sundrum II braneworld and Chern–Simons modified gravity in flat FRW universe. We discuss the cosmological parameters like equation of state parameter, deceleration parameter, squared speed of sound, Om-diagnostic and planes like evolving equation of state parameter and statefinders. These models yield useful results in this context.

In this short note, we will prove in a few steps that the new tetrads introduced previously in Einstein–Maxwell four-dimensional Lorentzian spacetimes, where gravitational and non-null electromagnetic fields are present, contain both the necessary information to provide the gravitational field and the necessary information to provide the electromagnetic field as well. These new tools thus become grand unification objects.

We introduce almost contact and cosymplectic Finsler manifolds. Then, we characterize almost contact Randers metrics. It is proved that a cosymplectic Finsler manifold of constant flag curvature must have vanishing flag curvature. We prove that every cosymplectic Finsler manifold is a Landsberg space, under a mild condition. Finally, we show that a cosymplectic Finsler manifold is a Douglas space if and only if it is a Berwald space.

In this paper, we study non-integrable distributions in a Riemannian manifold with a semi-symmetric metric connection, a kind of semi-symmetric non-metric connection and a statistical connection. We obtain the Gauss, Codazzi, and Ricci equations for non-integrable distributions with respect to the semi-symmetric metric connection, the semi-symmetric non-metric connection and the statistical connection. As applications, we obtain Chen’s inequalities for non-integrable distributions of real space forms endowed with a semi-symmetric metric connection and a kind of semi-symmetric non-metric connection. We give some examples of non-integrable distributions in a Riemannian manifold with affine connections. We find some new examples of Einstein distributions and distributions with constant scalar curvature.