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Search Results (6)

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Authors = Shyamal Kumar Hui ORCID = 0000-0001-5224-3467

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12 pages, 291 KiB  
Article
Eigenvalue of (p,q)-Biharmonic System along the Ricci Flow
by Lixu Yan, Yanlin Li, Apurba Saha, Abimbola Abolarinwa, Suraj Ghosh and Shyamal Kumar Hui
Axioms 2024, 13(5), 332; https://doi.org/10.3390/axioms13050332 - 17 May 2024
Viewed by 1154
Abstract
In this paper, we determine the variation formula for the first eigenvalue of (p,q)-biharmonic system on a closed Riemannian manifold. Several monotonic quantities are also derived. Full article
(This article belongs to the Special Issue Advances in Differential Geometry and Singularity Theory)
20 pages, 331 KiB  
Article
Contravariant Curvatures of Doubly Warped Product Poisson Manifolds
by Foued Aloui, Shyamal Kumar Hui and Ibrahim Al-Dayel
Mathematics 2024, 12(8), 1205; https://doi.org/10.3390/math12081205 - 17 Apr 2024
Cited by 2 | Viewed by 1019
Abstract
In this paper, we investigate the sectional contravariant curvature of a doubly warped product manifold ( fB×bF,g˜,Π=ΠB+ΠF) equipped with a product Poisson structure Π, using [...] Read more.
In this paper, we investigate the sectional contravariant curvature of a doubly warped product manifold ( fB×bF,g˜,Π=ΠB+ΠF) equipped with a product Poisson structure Π, using warping functions and sectional curvatures of its factor manifolds (B,g˜B,ΠB) and (F,g˜F,ΠF). Qualar and null sectional contravariant curvatures of ( fB×bF,g˜,Π) are also given. As an example, we construct a four-dimensional Lorentzian doubly warped product Poisson manifold where qualar and sectional curvatures are obtained. Full article
(This article belongs to the Special Issue Advances in Differential Geometry and Its Applications)
13 pages, 259 KiB  
Article
Contact CR-Warped Product Submanifold of a Sasakian Space Form with a Semi-Symmetric Metric Connection
by Meraj Ali Khan, Ibrahim Al-Dayel, Foued Aloui and Shyamal Kumar Hui
Symmetry 2024, 16(2), 190; https://doi.org/10.3390/sym16020190 - 6 Feb 2024
Cited by 1 | Viewed by 1313
Abstract
The main goal of this research paper is to investigate contact CR-warped product submanifolds within Sasakian space forms, utilizing a semi-symmetric metric connection. We conduct a comprehensive analysis of these submanifolds and establish several significant results. Additionally, we formulate an inequality that establishes [...] Read more.
The main goal of this research paper is to investigate contact CR-warped product submanifolds within Sasakian space forms, utilizing a semi-symmetric metric connection. We conduct a comprehensive analysis of these submanifolds and establish several significant results. Additionally, we formulate an inequality that establishes a relationship between the squared norm of the second fundamental form and the warping function. Lastly, we present a number of geometric applications derived from our findings. Full article
(This article belongs to the Special Issue Symmetry and Its Application in Differential Geometry and Topology, 3rd Edition)
14 pages, 319 KiB  
Article
Harnack Estimation for Nonlinear, Weighted, Heat-Type Equation along Geometric Flow and Applications
by Yanlin Li, Sujit Bhattacharyya, Shahroud Azami, Apurba Saha and Shyamal Kumar Hui
Mathematics 2023, 11(11), 2516; https://doi.org/10.3390/math11112516 - 30 May 2023
Cited by 24 | Viewed by 1862
Abstract
The method of gradient estimation for the heat-type equation using the Harnack quantity is a classical approach used for understanding the nature of the solution of these heat-type equations. Most of the studies in this field involve the Laplace–Beltrami operator, but in our [...] Read more.
The method of gradient estimation for the heat-type equation using the Harnack quantity is a classical approach used for understanding the nature of the solution of these heat-type equations. Most of the studies in this field involve the Laplace–Beltrami operator, but in our case, we studied the weighted heat equation that involves weighted Laplacian. This produces a number of terms involving the weight function. Thus, in this article, we derive the Harnack estimate for a positive solution of a weighted nonlinear parabolic heat equation on a weighted Riemannian manifold evolving under a geometric flow. Applying this estimation, we derive the Li–Yau-type gradient estimation and Harnack-type inequality for the positive solution. A monotonicity formula for the entropy functional regarding the estimation is derived. We specify our results for various different flows. Our results generalize some works. Full article
(This article belongs to the Special Issue Mathematical Modelling, Nonlinear Optimization, Nondimensionalization and Engineering Applications)
15 pages, 312 KiB  
Article
Li–Yau-Type Gradient Estimate along Geometric Flow
by Shyamal Kumar Hui, Abimbola Abolarinwa, Meraj Ali Khan, Fatemah Mofarreh, Apurba Saha and Sujit Bhattacharyya
Mathematics 2023, 11(6), 1364; https://doi.org/10.3390/math11061364 - 10 Mar 2023
Cited by 3 | Viewed by 2083
Abstract
In this article we derive a Li–Yau-type gradient estimate for a generalized weighted parabolic heat equation with potential on a weighted Riemannian manifold evolving by a geometric flow. As an application, a Harnack-type inequality is also derived in the end. Full article
(This article belongs to the Special Issue Differential Geometry: Structures on Manifolds and Submanifolds)
16 pages, 298 KiB  
Article
Evolution for First Eigenvalue of LT,f on an Evolving Riemannian Manifold
by Apurba Saha, Shahroud Azami, Daniel Breaz, Eleonora Rapeanu and Shyamal Kumar Hui
Mathematics 2022, 10(23), 4614; https://doi.org/10.3390/math10234614 - 5 Dec 2022
Cited by 2 | Viewed by 1520
Abstract
In this paper, evolution formulas for the first non-zero eigenvalue of the operator LT,f on a weighted closed Riemannian manifold along the Ricci flow as well as along the Yamabe flow are formulated. Some monotonic quantities are also derived for [...] Read more.
In this paper, evolution formulas for the first non-zero eigenvalue of the operator LT,f on a weighted closed Riemannian manifold along the Ricci flow as well as along the Yamabe flow are formulated. Some monotonic quantities are also derived for the normalized Ricci flow on Bianchi classes. Full article
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