arXiv subjects

Nasser Bin Turki

Publications and source records attributed to Nasser Bin Turki.

4 recordsLinked to original sources

arXiv2022

Perfect fluid spacetimes and gradient solitons

This article deals with the investigation of perfect fluid spacetimes endowed with concircular vector field. It is shown that in a perfect fluid spacetime with concircular vector field, the velocity vector field annihilates the conformal curvature tensor and in dimension 4, a perfect fluid spacetime is a generalized Robertson-Walker spacetime with Einstein fibre. Moreover, we prove that if a perfect fluid spacetime equipped with concircular vector field admits a second order symmetric parallel tensor, then either the state equation of the perfect fluid spacetime is characterized by $p=\frac{3-n}{n-1}σ$ , or the tensor is a constant multiple of the metric tensor. We also characterize the perfect fluid spacetimes with concircular vector field whose Lorentzian metrics are Ricci soliton, gradient Ricci soliton, gradient Yamabe solitons and gradient $m$-quasi Einstein solitons, respectively.

gr-qc↗

arXiv2020

On the Notion of a Generalized Mapping on Multiset Spaces

This work presents a generalized notion of multiset mapping thus resolving a long standing obstacle in structural study of multiset processing. It has been shown that the mapping defined herein can model a vast array of notions as special cases and also handels diverse situations in multiset rewriting transformations. Specifically, this paper unifies and generalizes the works of Parikh(1966), Hickman(1980), Khomenko(2003) and Nazmul(2013).

math.LO↗

arXiv2019

Two series of polyhedral fundamental domains for Lorentz bi-quotients

The main aim of this paper is to give two infinite series of examples of Lorentz space forms that can be obtained from Lorentz polyhedra by identification of faces. These Lorentz space forms are bi-quotients of the form $Γ_1\backslash G/Γ_2$, where $G=\widetilde{\operatorname{SU}(1,1)}\cong\widetilde{\operatorname{SL}(2,{\mathbb R})}$ is a simply connected Lie group with the Lorentz metric given by the Killing form, $Γ_1$ and $Γ_2$ are discrete subgroups of $G$ and $Γ_2$ is cyclic. A construction of polyhedral fundamental domains for the action of $Γ_1\timesΓ_2$ on $G$ via $(g,h)\cdot x=gxh^{-1}$ was given in the earlier work of the second author. In this paper we give an explicit description of the fundamental domains obtained by this construction for two infinite series of groups. These results are connected to singularity theory as the bi-quotients $Γ_1\backslash G/Γ_2$ appear as links of certain quasi-homogeneous $\mathbb Q$-Gorenstein surface singularities, i.e.\ the intersections of the singular variety with sufficiently small spheres around the isolated singular point.

math.DG↗

arXiv2018

Conformal vector fields and Yamabe solitons

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 of Yamabe metrics.

math.DG↗