arXiv subjects

Akram Ali

Publications and source records attributed to Akram Ali.

7 recordsLinked to original sources

arXiv2025

Transitioning late-time cosmology with the Hubble parameterization

We investigate a late-time cosmological model for a homogeneous and isotropic space-time in the Rastall theory. We explore the observational constraints on the Hubble parameter by using the latest cosmological datasets such as cosmic microwave background radiation (Planck), baryon acoustic oscillations (DESI) and Type Ia Supernovae (Union 3.0). As a result, we explicitly demonstrate that the specific redshift transition occurs, namely, there happens a phase shift in the evolution of the universe from the initial deceleration era to the current accelerating phase of the cosmological scenario. Furthermore, we show that with the latest dataset of DESI-BAO clubbed with CC, CMB, and Union 3.0, the current value of the Hubble parameter is estimated as $H_0 = 66.945 \pm 1.094$, which can be compatible with the available observations.

gr-qc↗

arXiv2025

Traversable Wormhole Solutions in massive $F(T)$ gravity

We study traversable wormhole geometries in an $F(T)$ teleparallel framework augmented by a perturbative de Rham-Gabadadze-Tolley (dRGT) graviton-mass term. Adopting the static, spherically symmetric Morris-Thorne ansatz, we derive the field and conservation equations and decompose the effective energy-momentum tensor into torsional and massive contributions. Focusing on three representative redshift profiles, namely, constant, logarithmic, and power-law, together with two realizations of the massive sector (the general case and a uniform-pressure specialization), we construct exact, horizonless solutions that satisfy the Morris-Thorne flaring-out condition and are asymptotically flat. The effective matter sector either respects the standard energy conditions or only mildly violates them within controlled parameter ranges. Crucially, the dRGT term supplies an additional anisotropic pressure that can sustain the throat without invoking explicitly exotic matter; in the vanishing-mass limit, the configurations reduce smoothly to standard $F(T)$ wormholes, confirming the internal consistency of the framework.

gr-qc↗

arXiv2021

$m$-quasi Einstein manifolds with convex potential

The main objective of this paper is to investigate the $m$-quasi Einstein manifold when the potential function becomes convex. In this article, it is proved that an $m$-quasi Einstein manifold satisfying some integral conditions with vanishing Ricci curvature along the direction of potential vector field has constant scalar curvature and hence the manifold turns out to be an Einstein manifold. It is also shown that in an $m$-quasi Einstein manifold the potential function agrees with Hodge-de Rham potential up to a constant. Finally, it is proved that if a complete non-compact and non-expanding $m$-quasi Einstein manifold has bounded scalar curvature and the potential vector field has global finite norm, then the scalar curvature vanishes.

math.DG↗

arXiv2021

Geometry of almost contact metrics as almost $*$-Ricci solitons

In the present paper, we give some characterizations by considering $*$-Ricci soliton as a Kenmotsu metric. We prove that if a Kenmotsu manifold represents an almost $*$-Ricci soliton with the potential vector field $V$ is a Jacobi along the Reeb vector field, then it is a steady $*$-Ricci soliton. Next, we show that a Kenmotsu matric endowed an almost $*$-Ricci soliton is Einstein metric if it is $\eta$-Einstein or the potential vector field $V$ is collinear to the Reeb vector field or $V$ is an infinitesimal contact transformation.

math.DG↗

arXiv2019

Curvature properties of Melvin magnetic metric

This paper aims to investigate the curvature restricted geometric properties admitted by Melvin magnetic spacetime metric, a warped product metric with $1$-dimensional fibre. For this, we have considered a Melvin type static, cylindrically symmetric spacetime metric in Weyl form and it is found that such metric, in general, is generalized Roter type, $Ein(3)$ and has pseudosymmetric Weyl conformal tensor satisfying the pseudosymmetric type condition $R\cdot R-Q(S,R)=\mathcal L' Q(g,C)$. The condition for which it satisfies the Roter type condition has been obtained. It is interesting to note that Melvin magnetic metric is pseudosymmetric and pseudosymmetric due to conformal tensor. Moreover such metric is $2$-quasi-Einstien, its Ricci tensor is Reimann compatible and Weyl conformal $2$-forms are recurrent. The Maxwell tensor is also pseudosymmetric type.

math.DG↗

arXiv2019

Geometry of statistical submanifolds of statistical warped product manifolds by optimization techniques

This paper deals with the applications of an optimization method on submanifolds, that is, geometric inequalities can be considered as optimization problems. In this regard, we obtain optimal Casorati inequalities and Chen-Ricci inequality for a statistical submanifold in a statistical warped product manifold of type $\mathbb{R} \times_{\mathfrak{f}} \overline{M}$ (almost Kenmotsu statistical manifold), where $\mathbb{R}$ and $\overline{M}$ are trivial statistical manifold and almost Kaehler statistical manifold, respectively.

math.DG↗

arXiv2019

Generalized inequalities of warped product submanifolds of nearly Kenmotsu $f$-manifolds

In the present paper, we discuss the non-trivial warped product pseudo slant submanifolds of type $M_{\bot }\times _{f}M_{\theta }$ and $M_{\theta}\times _{f}M_{\bot }$ of nearly Kenmotsu $f$-manifold $\overline{M}$. Firstly, we get some basic properties of these type warped product submanifolds. Then, we establish the general sharp inequalities for squared norm of second fundamental form for mixed totally geodesic warped product pseudo slant submanifolds of both cases, in terms of the warping function and the slant angle. Also the equality cases are verified. We show that some previous results are trivial from our results.

math.DG↗