Communications of the
Korean Mathematical Society
CKMS
ISSN(Print) 1225-1763
ISSN(Online) 2234-3024
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2023-10-31
Geometry of generalized Berger-type deformed metric on $B$-manifold
ABDERRAHIM ZAGANEAbstract : Let $(M^{2m},\varphi,g)$ be a $B$-manifold. In this paper, we introduce a new class of metric on $(M^{2m},\varphi,g)$, obtained by a non-conformal deformation of the metric $g$, called a generalized Berger-type deformed metric. First we investigate the Levi-Civita connection of this metric. Secondly we characterize the Riemannian curvature, the sectional curvature and the scalar curvature. Finally, we study the proper biharmonicity of the identity map and of a curve on $M$ with respect to a generalized Berger-type deformed metric.
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2023-07-31
Existence and nonexistence of solutions for a class of Hamiltonian strongly degenerate elliptic system
Nguyen Viet TuanAbstract : In this paper, we study the existence and nonexistence of solutions for a class of Hamiltonian strongly degenerate elliptic system with subcritical growth \begin{equation*} \begin{cases} -\Delta_\lambda u -\mu v =|v|^{p-1}v &\;\text{ in } \Omega,\\ -\Delta_\lambda v -\mu u=|u|^{q-1}u &\;\text{ in } \Omega,\\ u = v = 0 &\;\text{ on } \partial\Omega, \end{cases} \end{equation*} where $p, q>1$ and $\Omega$ is a smooth bounded domain in $\mathbb{R}^N$, $N\ge 3$. Here $\Delta_\lambda$ is the strongly degenerate elliptic operator. The existence of at least a nontrivial solution is obtained by variational methods while the nonexistence of positive solutions are proven by a contradiction argument.
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2022-10-31
Jordan $\mathcal{G}_n$-derivations on path algebras
Abderrahim Adrabi, Driss Bennis, Brahim FahidAbstract : Recently, Bre\v{s}ar's Jordan $\{g,h\}$-derivations have been investigated on triangular algebras. As a first aim of this paper, we extend this study to an interesting general context. Namely, we introduce the notion of Jordan $\mathcal{G}_n$-derivations, with $n \ge 2$, which is a natural generalization of Jordan $\{g,h\}$-derivations. Then, we study this notion on path algebras. We prove that, when $n > 2$, every Jordan $\mathcal{G}_n$-derivation on a path algebra is a $\{g,h\}$-derivation. However, when $n = 2$, we give an example showing that this implication does not hold true in general. So, we characterize when it holds. As a second aim, we give a positive answer to a variant of Lvov-Kaplansky conjecture on path algebras. Namely, we show that the set of values of a multi-linear polynomial on a path algebra $KE$ is either $\{0\}$, $KE$ or the space spanned by paths of a length greater than or equal to $1$.
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2024-01-31
Spacetimes admitting divergence free $m$-projective curvature tensor
Uday Chand De, Dipankar HazraAbstract : This paper is concerned with the study of spacetimes satisfying $\mathrm{div}\mathcal{M}=0$, where ``div" denotes the divergence and $\mathcal{M}$ is the $m$-projective curvature tensor. We establish that a perfect fluid spacetime with $\mathrm{div}\mathcal{M}=0$ is a generalized Robertson-Walker spacetime and vorticity free; whereas a four-dimensional perfect fluid spacetime becomes a Robertson-Walker spacetime. Moreover, we establish that a Ricci recurrent spacetime with $\mathrm{div}\mathcal{M}=0$ represents a generalized Robertson-Walker spacetime.
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2024-01-31
Some remarks on $S$-valuation domains
Ali Benhissi, Abdelamir DabbabiAbstract : Let $A$ be a commutative integral domain with identity element and $S$ a multiplicatively closed subset of $A$. In this paper, we introduce the concept of $S$-valuation domains as follows. The ring $A$ is said to be an $S$-valuation domain if for every two ideals $I$ and $J$ of $A$, there exists $s\in S$ such that either $sI\subseteq J$ or $sJ\subseteq I$. We investigate some basic properties of $S$-valuation domains. Many examples and counterexamples are provided.
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2023-10-31
Remarks on the gradient flow of $\alpha$ energy potential on the line
Hyojun An, Hyungjin HuhAbstract : We are interested in the gradient flow of $\alpha$ energy potential. We provide basic estimates and study asymptotic behaviors for the case $N=2, \ldots, 5$.
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2024-01-31
Some results related to differential-difference counterpart of the Br\"{u}ck conjecture
Md. Adud, BIKASH CHAKRABORTYAbstract : In this paper, our focus is on exploring value sharing \linebreak problems related to a transcendental entire function $f$ and its associated differential-difference polynomials. We aim to establish some results which are related to differential-difference counterpart of the Br\"{u}ck conjecture.
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2023-10-31
The flow-curvature of curves in a geometric surface
Mircea CrasmareanuAbstract : For a fixed parametrization of a curve in an orientable two-dimensional Riemannian manifold, we introduce and investigate a new frame and curvature function. Due to the way of defining this new frame as being the time-dependent rotation in the tangent plane of the standard Frenet frame, both these new tools are called flow.
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2023-10-31
Soliton functions and Ricci curvatures of $D$-homothetically deformed $f$-Kenmotsu almost Riemann solitons
Urmila Biswas, Avijit SarkarAbstract : The present article contains the study of $D$-homothetically deformed $f$-Kenmotsu manifolds. Some fundamental results on the deformed spaces have been deduced. Some basic properties of the Riemannian metric as an inner product on both the original and deformed spaces have been established. Finally, applying the obtained results, soliton functions, Ricci curvatures and scalar curvatures of almost Riemann solitons with several kinds of potential vector fields on the deformed spaces have been characterized.
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2023-10-31
Laplace transform and Hyers-Ulam stability of differential equation for logistic growth in a population model
Ponmana Selvan Arumugam, Ganapathy Gandhi, Saravanan Murugesan, Veerasivaji RamachandranAbstract : In this paper, we prove the Hyers-Ulam stability and Mittag-Leffler-Hyers-Ulam stability of a differential equation of Logistic growth in a population by applying Laplace transforms method.
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Some results on the geometry of a non-conformal deformation of a metric
Nour Elhouda Djaa, Abderrahim Zagane
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Miao-Tam equation on almost coK"{a}hler manifolds
Tarak Mandal
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On the 2-absorbing submodules and zero-divisor graph of equivalence classes of zero divisors
Shiroyeh Payrovi, Yasaman Sadatrasul
Commun. Korean Math. Soc. 2023; 38(1): 39-46
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Properties of functions with bounded rotation associated with lima\c{c}on class
Kanwal Jabeen, Afis Saliu
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On the rational cohomology of mapping spaces and their realization problem
Abdelhadi Zaim
Commun. Korean Math. Soc. 2023; 38(4): 1309-1320
https://doi.org/10.4134/CKMS.c230014 -
On nonnil-SFT rings
Ali Benhissi, Abdelamir Dabbabi
Commun. Korean Math. Soc. 2023; 38(3): 663-677
https://doi.org/10.4134/CKMS.c220230 -
$\star$-conformal Ricci solitons on almost coK\"{a}hler manifolds
Tarak Mandal, Avijit Sarkar
Commun. Korean Math. Soc. 2023; 38(3): 865-880
https://doi.org/10.4134/CKMS.c220145 -
Results concerning semi-symmetric metric $F$-connections on the Hsu-$B$ manifolds
Uday Chand De, Aydin Gezer, Cagri Karaman
Commun. Korean Math. Soc. 2023; 38(3): 837-846
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