Norah Alshehri
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Research Subjects
Norah Alshehri has a total of 10 co-authors. Here are the top co-authors by number of shared publications:
- Mohammed Guediri
Department of Mathematics, College of Sciences, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia
9 shared publications - Akram Ali
Department of Mathematics, College of Sciences, King Khalid University, Abha 61413, Saudi Arabia
6 shared publications - Fatemah Mofarreh
Mathematical Science Department, College of Science, Princess Nourah Bint Abdulrahman University, Riyadh, Saudi Arabia
3 shared publications - Yanlin Li
School of Mathematics, Hangzhou Normal University, Hangzhou 311121, China
3 shared publications Mohammed Guediri
Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia
2 shared publications- Abimbola Abolarinwa
Department of Mathematics, University of Lagos, Akoka, Lagos State, Nigeria
1 shared publication
Latest Publications
- Open Access
- 1 October 2026
- Published by MDPI AG in Mathematics
- Vol. 14 (19) , 3568
A Method Using Differential Equations for Characterizing Warped Product Lagrangian Submanifolds in Complex Space Forms
In this paper, we establish new inequalities for the length of the second fundamental form of an n-dimensional compact warped product Lagrangian submanifold in a complex space form . These estimates are expressed in terms of the Laplacian and the gradient of the warping function, together with a positive lower bound on the Ricci curvature. To the best of our knowledge, this provides the first nontrivial result of this type obtained without imposing higher-order curvature assumptions. The characterization results are derived using Obata-type and Tashiro-type differential equations on suitable Riemannian manifolds. By combining the Bochner formula with second-order differential equation techniques, we further characterize the warped product via the first nonzero eigenvalue associated with the warping function. In particular, under appropriate conditions on the second fundamental form, we show that is isometric to either the Euclidean space or the standard sphere .- 1 October 2026
- Published by MDPI AG in Mathematics
- Vol. 14 (19) , 3568
Open AccessA Method Using Differential Equations for Characterizing Warped Product Lagrangian Submanifolds in Complex Space Forms
In this paper, we establish new inequalities for the length of the second fundamental form of an n-dimensional compact warped product Lagrangian submanifold in a complex space form . These estimates are expressed in terms of the Laplacian and the gradient of the warping function, together with a positive lower bound on the Ricci curvature. To the best of our knowledge, this provides the first nontrivial result of this type obtained without imposing higher-order curvature assumptions. The characterization results are derived using Obata-type and Tashiro-type differential equations on suitable Riemannian manifolds. By combining the Bochner formula with second-order differential equation techniques, we further characterize the warped product via the first nonzero eigenvalue associated with the warping function. In particular, under appropriate conditions on the second fundamental form, we show that is isometric to either the Euclidean space or the standard sphere . - Open Access
- 5 August 2026
- Published by MDPI AG in Mathematics
- Vol. 14 (15) , 2809
Rigidity and Classification of Ricci Solitons on Lorentzian Hypersurfaces with Concircular Vector Fields on Minkowski Space
This paper examines the classification of Lorentzian hypersurfaces in Minkowski space, specifically focusing on those that are characterized as good or bad and that admit Ricci solitons with a concircular vector field. First, we demonstrate that Ricci solitons of this nature do not exist in Lorentzian spaces that have non-zero sectional curvature. Additionally, we show that the shape operator can be expressed in specific canonical forms.
- 5 August 2026
- Published by MDPI AG in Mathematics
- Vol. 14 (15) , 2809
Open AccessRigidity and Classification of Ricci Solitons on Lorentzian Hypersurfaces with Concircular Vector Fields on Minkowski Space
This paper examines the classification of Lorentzian hypersurfaces in Minkowski space, specifically focusing on those that are characterized as good or bad and that admit Ricci solitons with a concircular vector field. First, we demonstrate that Ricci solitons of this nature do not exist in Lorentzian spaces that have non-zero sectional curvature. Additionally, we show that the shape operator can be expressed in specific canonical forms.
- Open Access
Closed Conformal Vector Fields in Gradient Einstein Solitons
We investigate gradient Einstein solitons admitting closed conformal vector fields. Under constant scalar curvature, we establish rigidity results showing that complete solitons with non-parallel closed conformal vector fields are isometric to Euclidean space. In the non-compact case, we prove that solitons with homothetic closed conformal vector fields are locally conformally flat in dimension four and possess a harmonic Weyl tensor in higher dimensions. Furthermore, we obtain a classification result, showing that such solitons admit a warped product structure with a one-dimensional base and space form fibers.
Open AccessClosed Conformal Vector Fields in Gradient Einstein Solitons
We investigate gradient Einstein solitons admitting closed conformal vector fields. Under constant scalar curvature, we establish rigidity results showing that complete solitons with non-parallel closed conformal vector fields are isometric to Euclidean space. In the non-compact case, we prove that solitons with homothetic closed conformal vector fields are locally conformally flat in dimension four and possess a harmonic Weyl tensor in higher dimensions. Furthermore, we obtain a classification result, showing that such solitons admit a warped product structure with a one-dimensional base and space form fibers.
- Open Access
- 1 January 2026
- Published by American Institute of Mathematical Sciences (AIMS) in AIMS Mathematics
- Vol. 11 (8) , 27396-27410
Rigidity of almost Ricci solitons with affine vector fields on semi-Riemannian manifolds
We investigated almost Ricci solitons on semi-Riemannian manifolds when the potential vector field was affine. Our central theorem showed that in every dimension $ n \geq 3 $, such almost Ricci solitons coincide with Ricci solitons, and the manifolds had constant scalar curvature. In contrast, in dimension 2, we constructed explicit examples of proper (but trivial) almost Ricci solitons, highlighting a genuine low dimensional distinction. In the Riemannian setting, this leads to rigidity: Under natural geometric assumptions, an almost Ricci soliton must be parallel, trivial, or Ricci-flat.- 1 January 2026
- Published by American Institute of Mathematical Sciences (AIMS) in AIMS Mathematics
- Vol. 11 (8) , 27396-27410
Open AccessRigidity of almost Ricci solitons with affine vector fields on semi-Riemannian manifolds
We investigated almost Ricci solitons on semi-Riemannian manifolds when the potential vector field was affine. Our central theorem showed that in every dimension $ n \geq 3 $, such almost Ricci solitons coincide with Ricci solitons, and the manifolds had constant scalar curvature. In contrast, in dimension 2, we constructed explicit examples of proper (but trivial) almost Ricci solitons, highlighting a genuine low dimensional distinction. In the Riemannian setting, this leads to rigidity: Under natural geometric assumptions, an almost Ricci soliton must be parallel, trivial, or Ricci-flat. - Open Access
- 25 August 2025
- Published by MDPI AG in Mathematics
- Vol. 13 (17) , 2725
Impact of Ambient Conformal Vector Fields on Yamabe Solitons on Riemannian Hypersurfaces
We investigate Yamabe solitons on Riemannian hypersurfaces induced by conformal vector fields in Riemannian and Lorentzian manifolds, with an emphasis on the tangential component. We show that these hypersurfaces are totally umbilical, and when the ambient manifold is Einstein, a rigidity condition emerges connecting the mean and scalar curvatures. Using this, we classify compact Yamabe solitons: each hypersurface is either totally geodesic or an extrinsic sphere. Additionally, we prove the non-existence of trivial Yamabe solitons on oriented hypersurfaces of higher dimension in Einstein manifolds. These results highlight the classification of compact hypersurfaces and rigidity phenomena in the ambient spaces, providing a clear understanding of the geometric structures associated with Yamabe solitons.
- 25 August 2025
- Published by MDPI AG in Mathematics
- Vol. 13 (17) , 2725
Open AccessImpact of Ambient Conformal Vector Fields on Yamabe Solitons on Riemannian Hypersurfaces
We investigate Yamabe solitons on Riemannian hypersurfaces induced by conformal vector fields in Riemannian and Lorentzian manifolds, with an emphasis on the tangential component. We show that these hypersurfaces are totally umbilical, and when the ambient manifold is Einstein, a rigidity condition emerges connecting the mean and scalar curvatures. Using this, we classify compact Yamabe solitons: each hypersurface is either totally geodesic or an extrinsic sphere. Additionally, we prove the non-existence of trivial Yamabe solitons on oriented hypersurfaces of higher dimension in Einstein manifolds. These results highlight the classification of compact hypersurfaces and rigidity phenomena in the ambient spaces, providing a clear understanding of the geometric structures associated with Yamabe solitons.
- Open Access
Ricci Solitons on Riemannian Hypersurfaces Generated by Torse-Forming Vector Fields in Riemannian and Lorentzian Manifolds
In this paper, we examine torse-forming vector fields to characterize extrinsic spheres (that is, totally umbilical hypersurfaces with nonzero constant mean curvatures) in Riemannian and Lorentzian manifolds. First, we analyze the properties of these vector fields on Riemannian manifolds. Next, we focus on Ricci solitons on Riemannian hypersurfaces induced by torse-forming vector fields of Riemannian or Lorentzian manifolds. Specifically, we show that such a hypersurface in the manifold with constant sectional curvature is either totally geodesic or an extrinsic sphere.
Open AccessRicci Solitons on Riemannian Hypersurfaces Generated by Torse-Forming Vector Fields in Riemannian and Lorentzian Manifolds
In this paper, we examine torse-forming vector fields to characterize extrinsic spheres (that is, totally umbilical hypersurfaces with nonzero constant mean curvatures) in Riemannian and Lorentzian manifolds. First, we analyze the properties of these vector fields on Riemannian manifolds. Next, we focus on Ricci solitons on Riemannian hypersurfaces induced by torse-forming vector fields of Riemannian or Lorentzian manifolds. Specifically, we show that such a hypersurface in the manifold with constant sectional curvature is either totally geodesic or an extrinsic sphere.
- Open Access
- 1 January 2025
- Published by National Library of Serbia in Filomat
- Vol. 39 (21) , 7347-7357
On gradient Ricci-Bourguignon harmonic solitons in sequential warped products
Our investigation involves sequential warped product manifolds that contain gradient Ricci-Bourguignon harmonic solutions. We present the primary connections for a gradient Ricci-Bourguignon harmonic solution on sequential warped product manifolds. In practical applications, our research inves-tigates gradient Ricci-Bourguignon harmonic solitons for sequential generalized Robertson-Walker space-times and sequential standard static spacetimes. Our finding generalizes all results proven in [23].
- 1 January 2025
- Published by National Library of Serbia in Filomat
- Vol. 39 (21) , 7347-7357
Open AccessOn gradient Ricci-Bourguignon harmonic solitons in sequential warped products
Our investigation involves sequential warped product manifolds that contain gradient Ricci-Bourguignon harmonic solutions. We present the primary connections for a gradient Ricci-Bourguignon harmonic solution on sequential warped product manifolds. In practical applications, our research inves-tigates gradient Ricci-Bourguignon harmonic solitons for sequential generalized Robertson-Walker space-times and sequential standard static spacetimes. Our finding generalizes all results proven in [23].
- Open Access
- 1 January 2025
- Published by American Institute of Mathematical Sciences (AIMS) in AIMS Mathematics
- Vol. 10 (6) , 13524-13539
Rigidity of almost Ricci solitons on compact Riemannian manifolds
Considering an almost Ricci soliton (ARS) $ \left(N, g, \eta, \kappa \right) $ on a compact Riemannian manifold $ (N, g) $, we use the Ricci curvature in the direction of the potential vector field $ \eta $ to derive necessary and sufficient conditions for $ (N, g) $ to be isometric to a sphere. This expands on several recent results regarding Ricci solitons and almost Ricci solitons by applying specific integral inequalities involving the Ricci curvature evaluated in the direction $ \eta $. Furthermore, we present conditions under which $ \eta $ is either Killing or parallel; in particular, the ARS is trivial.- 1 January 2025
- Published by American Institute of Mathematical Sciences (AIMS) in AIMS Mathematics
- Vol. 10 (6) , 13524-13539
Open AccessRigidity of almost Ricci solitons on compact Riemannian manifolds
Considering an almost Ricci soliton (ARS) $ \left(N, g, \eta, \kappa \right) $ on a compact Riemannian manifold $ (N, g) $, we use the Ricci curvature in the direction of the potential vector field $ \eta $ to derive necessary and sufficient conditions for $ (N, g) $ to be isometric to a sphere. This expands on several recent results regarding Ricci solitons and almost Ricci solitons by applying specific integral inequalities involving the Ricci curvature evaluated in the direction $ \eta $. Furthermore, we present conditions under which $ \eta $ is either Killing or parallel; in particular, the ARS is trivial. - Open Access
- 17 December 2024
- Published by MDPI AG in Mathematics
- Vol. 12 (24) , 3958
Correction: Alshehri, N.; Guediri, M. Projective Vector Fields on Semi-Riemannian Manifolds. Mathematics 2024, 12, 2914
In our recent paper [1], we stated in Theorem 10 that on an n-dimensional semi-Riemannian manifold with , if P is a projective vector field that is also conformal, satisfying , and the vector field , dual to , maintains a consistent causal character, then either P is homothetic or is light-like- 17 December 2024
- Published by MDPI AG in Mathematics
- Vol. 12 (24) , 3958
Open AccessCorrection: Alshehri, N.; Guediri, M. Projective Vector Fields on Semi-Riemannian Manifolds. Mathematics 2024, 12, 2914
In our recent paper [1], we stated in Theorem 10 that on an n-dimensional semi-Riemannian manifold with , if P is a projective vector field that is also conformal, satisfying , and the vector field , dual to , maintains a consistent causal character, then either P is homothetic or is light-like - Open Access
Characterizing Affine Vector Fields on Pseudo-Riemannian Manifolds
We study the characteristics of affine vector fields on pseudo-Riemannian manifolds and provide tensorial formulas that characterize these vector fields. Using our approach, we present a straightforward proof that any affine vector field on a compact Riemannian manifold is a Killing vector field. Moreover, we establish several necessary and sufficient conditions for an affine vector field on a Riemannian manifold to be classified as a Killing or parallel vector field.
Open AccessCharacterizing Affine Vector Fields on Pseudo-Riemannian Manifolds
We study the characteristics of affine vector fields on pseudo-Riemannian manifolds and provide tensorial formulas that characterize these vector fields. Using our approach, we present a straightforward proof that any affine vector field on a compact Riemannian manifold is a Killing vector field. Moreover, we establish several necessary and sufficient conditions for an affine vector field on a Riemannian manifold to be classified as a Killing or parallel vector field.