On the Topology of Warped Product Pointwise Semi-Slant Submanifolds with Positive Curvature by Yanlin Li, Ali H. Alkhaldi, Akram Ali, Pişcoran Laurian-Ioan

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Investigation of ruled surfaces and their singularities according to Blaschke frame in Euclidean 3-space by Yanlin Li, Ali. H. Alkhaldi, Akram Ali, R. A. Abdel-Baky, M. Khalifa Saad

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Characterization of Almost Yamabe Solitons and Gradient Almost Yamabe Solitons with Conformal Vector Fields by Ali H. Alkhaldi, Pişcoran Laurian-Ioan, Abimbola Abolarinwa, Akram Ali

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Characterizing Base in Warped Product Submanifolds of Complex Projective Spaces by Differential Equations by Ali H. Alkhaldi, Pişcoran Laurian-Ioan, Izhar Ahmad, Akram Ali

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Chen Inequalities for Warped Product Pointwise Bi-Slant Submanifolds of Complex Space Forms and Its Applications by Akram Ali, Ali H. Alkhaldi

Subjects: “…mean curvature…”
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An Invariant of Riemannian Type for Legendrian Warped Product Submanifolds of Sasakian Space Forms by Fatemah Abdullah Alghamdi, Lamia Saeed Alqahtani, Ali H. Alkhaldi, Akram Ali

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Bounds for Eigenvalues of <i>q</i>-Laplacian on Contact Submanifolds of Sasakian Space Forms by Yanlin Li, Fatemah Mofarreh, Abimbola Abolarinwa, Norah Alshehri, Akram Ali

“…This study establishes new upper bounds for the mean curvature and constant sectional curvature on Riemannian manifolds for the first positive eigenvalue of the <i>q</i>-Laplacian. …”
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Reilly-type inequality for the Φ-Laplace operator on semislant submanifolds of Sasakian space forms by Yanlin Li, Fatemah Mofarreh, Ravi P. Agrawal, Akram Ali

“…Abstract This paper aims to establish new upper bounds for the first positive eigenvalue of the Φ-Laplacian operator on Riemannian manifolds in terms of mean curvature and constant sectional curvature. The first eigenvalue for the Φ-Laplacian operator on closed oriented m-dimensional semislant submanifolds in a Sasakian space form M ˜ 2 k + 1 ( ϵ ) is estimated in various ways. …”
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The eigenvalues of β-Laplacian of slant submanifolds in complex space forms by Lamia Saeed Alqahtani, Akram Ali

“…In this paper, we provided various estimates of the first nonzero eigenvalue of the $ \beta $-Laplacian operator on closed orientated $ p $-dimensional slant submanifolds of a $ 2m $-dimensional complex space form $ \widetilde{\mathbb{V}}^{2m}(4\epsilon) $ with constant holomorphic sectional curvature $ 4\epsilon $. As applications of our results, we generalized the Reilly-inequality for the Laplacian to the $ \beta $-Laplacian on slant submanifolds of a complex Euclidean space and a complex projective space.…”
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Estimation of inequalities for warped product semi-slant submanifolds of Kenmotsu space forms by Misbah Liaqat, Piscoran Laurian-Ioan, Wan Ainun Mior Othman, Akram Ali, Abdullah Gani, Cenap Ozel

“…Abstract In this paper, we construct the geometric inequalities for the squared norm of the mean curvature and warping functions of warped product semi-slant submanifolds in Kenmotsu space forms. …”
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Geometry of <em>k</em>-Yamabe Solitons on Euclidean Spaces and Its Applications to Concurrent Vector Fields by Akram Ali, Fatemah Mofarreh, Pişcoran Laurian-Ioan, Nadia Alluhaibi

“…We provide an example to support this study and all of the results in this paper can be implemented to Yamabe solitons for <i>k</i>-curvature with <inline-formula><math display="inline"><semantics><mrow><mi>k</mi><mo>=</mo><mn>1</mn></mrow></semantics></math></inline-formula>.…”
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Null Homology Groups and Stable Currents in Warped Product Submanifolds of Euclidean Spaces by Yanlin Li, Pişcoran Laurian-Ioan, Akram Ali, Ali H. Alkhaldi

“…In this paper, we prove that, for compact warped product submanifolds <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>M</mi><mi>n</mi></msup></semantics></math></inline-formula> in an Euclidean space <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi mathvariant="double-struck">E</mi><mrow><mi>n</mi><mo>+</mo><mi>k</mi></mrow></msup></semantics></math></inline-formula>, there are no stable <i>p</i>-currents, homology groups are vanishing, and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>M</mi><mn>3</mn></msup></semantics></math></inline-formula> is homotopic to the Euclidean sphere <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi mathvariant="double-struck">S</mi><mn>3</mn></msup></semantics></math></inline-formula> under various extrinsic restrictions, involving the eigenvalue of the warped function, integral Ricci curvature, and the Hessian tensor. The results in this paper can be considered an extension of Xin’s work in the framework of a compact warped product submanifold, when the base manifold is minimal in ambient manifolds.…”
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General Relativistic Space-Time with <i>η</i>₁-Einstein Metrics by Yanlin Li, Fatemah Mofarreh, Santu Dey, Soumendu Roy, Akram Ali

“…In adition, certain curvature conditions on the space-time that admit an <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>η</mi><mn>1</mn></msub></semantics></math></inline-formula>-Einstein soliton are explored and build up the importance of the Laplace equation on the space-time in terms of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>η</mi><mn>1</mn></msub></semantics></math></inline-formula>-Einstein soliton. …”
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Ricci Soliton of <inline-formula><math display="inline"><semantics><mi mathvariant="script">CR</mi></semantics></math></inline-formula>-Warped Product Manifolds and Their Classific... by Yanlin Li, Sachin Kumar Srivastava, Fatemah Mofarreh, Anuj Kumar, Akram Ali

“…We also derive some characterizations of Einstein warped product manifolds under the impact of Ricci Curvature and Divergence of Hessian tensor.…”
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The Homology of Warped Product Submanifolds of Spheres and Their Applications by Lamia Saeed Alqahtani, Akram Ali, Pişcoran Laurian-Ioan, Ali H. Alkhaldi

“…The constraints are also applied to the warped function eigenvalues and integral Ricci curvatures.…”
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