Nasser Bin Turki

Bio: Nasser Bin Turki is an academic researcher from King Saud University. The author has contributed to research in topics: Vector field & Soliton. The author has an hindex of 4, co-authored 20 publications receiving 40 citations.

Geodesic Vector Fields on a Riemannian Manifold

Abstract: A unit geodesic vector field on a Riemannian manifold is a vector field whose integral curves are geodesics, or in other worlds have zero acceleration. A geodesic vector field on a Riemannian manifold is a smooth vector field with acceleration of each of its integral curves is proportional to velocity. In this paper, we show that the presence of a geodesic vector field on a Riemannian manifold influences its geometry. We find characterizations of n-spheres as well as Euclidean spaces using geodesic vector fields.

Hypersurfaces of a Sasakian Manifold

Abstract: We extend the study of orientable hypersurfaces in a Sasakian manifold initiated by Watanabe. The Reeb vector field ξ of the Sasakian manifold induces a vector field ξ T on the hypersurface, namely the tangential component of ξ to hypersurface, and it also gives a smooth function ρ on the hypersurface, which is the projection of the Reeb vector field on the unit normal. First, we find volume estimates for a compact orientable hypersurface and then we use them to find an upper bound of the first nonzero eigenvalue of the Laplace operator on the hypersurface, showing that if the equality holds then the hypersurface is isometric to a certain sphere. Also, we use a bound on the energy of the vector field ∇ ρ on a compact orientable hypersurface in a Sasakian manifold in order to find another geometric condition (in terms of mean curvature and integral curves of ξ T ) under which the hypersurface is isometric to a sphere. Finally, we study compact orientable hypersurfaces with constant mean curvature in a Sasakian manifold and find a sharp upper bound on the first nonzero eigenvalue of the Laplace operator on the hypersurface. In particular, we show that this upper bound is attained if and only if the hypersurface is isometric to a sphere, provided that the Ricci curvature of the hypersurface along ∇ ρ has a certain lower bound.

A note on $$\varphi $$-analytic conformal vector fields

Abstract: Taking clue from the analytic vector fields on a complex manifold, $$\varphi \hbox {-analytic}$$ conformal vector fields are defined on a Riemannian manifold (Deshmukh and Al-Solamy in Colloq. Math. 112(1):157–161, 2008). In this paper, we use $$\varphi \hbox {-analytic}$$ conformal vector fields to find new characterizations of the n-sphere $$ S^{n}(c)$$ and the Euclidean space $$(R^{n},\left\langle ,\right\rangle )$$ .

Homotopy perturbation and Adomian decomposition methods for modeling the nonplanar structures in a bi-ion ionospheric superthermal plasma

Abstract: The propagation of cylindrical and spherical (nonplanar) electrostatic ion-acoustic waves (IAWs) in a collisionless, unmagnetized, and homogeneous plasma consisting of hot and cold positive ions as well as superthermal electrons are numerically investigated. The nonplanar Korteweg–de Vries (nKdV) equation is deduced from the fluid equations of the plasma species by employing the reductive perturbation technique. For studying the characteristics of the nonplanar electrostatic IAWs, both homotopy perturbation method (HPM) and Adomian decomposition method (ADM) are devoted for solving the nKdV equation numerically. For checking the accuracy of the obtained solutions, a comparison between the exact analytical solution and the approximate numerical solutions of the integrable case (planar KdV equation) is carried out. Moreover, the absolute error and both minimum and maximum residual errors of both ADM and HPM are estimated. Also, the effect of the physical plasma parameters on the characteristics of (non)planar soliton profiles is investigated. It is found that IAWs are significantly modified due to the presence of excess superthermal electrons and nonplanar geometry.

Some Results on Ricci Almost Solitons

Abstract: We find three necessary and sufficient conditions for an n-dimensional compact Ricci almost soliton (M,g,w,σ) to be a trivial Ricci soliton under the assumption that the soliton vector field w is a geodesic vector field (a vector field with integral curves geodesics). The first result uses condition r2≤nσr on a nonzero scalar curvature r; the second result uses the condition that the soliton vector field w is an eigen vector of the Ricci operator with constant eigenvalue λ satisfying n2λ2≥r2; the third result uses a suitable lower bound on the Ricci curvature S(w,w). Finally, we show that an n-dimensional connected Ricci almost soliton (M,g,w,σ) with soliton vector field w is a geodesic vector field with a trivial Ricci soliton, if and only if, nσ−r is a constant along integral curves of w and the Ricci curvature S(w,w) has a suitable lower bound.

Geodesic Vector Fields on a Riemannian Manifold

Abstract: A unit geodesic vector field on a Riemannian manifold is a vector field whose integral curves are geodesics, or in other worlds have zero acceleration. A geodesic vector field on a Riemannian manifold is a smooth vector field with acceleration of each of its integral curves is proportional to velocity. In this paper, we show that the presence of a geodesic vector field on a Riemannian manifold influences its geometry. We find characterizations of n-spheres as well as Euclidean spaces using geodesic vector fields.

On scalar curvature rigidity of Vacuum Static Spaces

Abstract: In this paper we extend the local scalar curvature rigidity result in [6] to a small domain on general vacuum static spaces, which confirms the interesting dichotomy of local surjectivity and local rigidity about the scalar curvature in general in the light of the paper [10]. We obtain the local scalar curvature rigidity of bounded domains in hyperbolic spaces. We also obtain the global scalar curvature rigidity for conformal deformations of metrics in the domains, where the lapse functions are positive, on vacuum static spaces with positive scalar curvature, and show such domains are maximal, which generalizes the work in [15].

A remarkable property of concircular vector fields on a Riemannian manifold

Abstract: In this paper, we show that, given a non-trivial concircular vector field u on a Riemannian manifold ( M , g ) with potential function f, there exists a unique smooth function ρ on M that connects u to the gradient of potential function ∇ f . We call the connecting function of the concircular vector field u. This connecting function is shown to be a main ingredient in obtaining characterizations of n-sphere S n ( c ) and the Euclidean space E n . We also show that the connecting function influences on a topology of the Riemannian manifold.