Communications of the
Korean Mathematical Society
CKMS

ISSN(Print) 1225-1763 ISSN(Online) 2234-3024

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  • 2023-10-31

    Transversal lightlike submersions from indefinite Sasakian manifolds onto lightlike manifolds

    Shiv Sharma Shukla, Vipul Singh

    Abstract : In this paper, we introduce and study two new classes of lightlike submersions, called radical transversal and transversal lightlike submersions between an indefinite Sasakian manifold and a lightlike manifold. We give examples and investigate the geometry of distributions involved in the definitions of these lightlike submersions. We also study radical transversal and transversal lightlike submersions from an indefinite Sasakian manifold onto a lightlike manifold with totally contact umbilical fibers.

  • 2022-07-31

    Chen invariants and statistical submanifolds

    Hitoshi Furuhata, Izumi Hasegawa, Naoto Satoh

    Abstract : We define a kind of sectional curvature and $delta$-invariants for statistical manifolds. For statistical submanifolds the sum of the squared mean curvature and the squared dual mean curvature is bounded below by using the $delta$-invariant. This inequality can be considered as a generalization of the so-called Chen inequality for Riemannian submanifolds.

  • 2022-10-31

    Note on the multifractal measures of Cartesian product sets

    Najmeddine Attia, Rihab Guedri, Omrane Guizani

    Abstract : In this paper, we shall be concerned with evaluation of multifractal Hausdorff measure ${\mathcal H}^{q,t}_\mu$ and multifractal packing measure ${\mathcal P}^{q,t}_\mu$ of Cartesian product sets by means of the measure of their components. This is done by investigating the density result introduced in \cite{Olsen95}. As a consequence, we get the inequalities related to the multifractal dimension functions, proved in \cite{Olsen96}, by using a unified method for all the inequalities. Finally, we discuss the extension of our approach to studying the multifractal Hewitt-Stromberg measures of Cartesian product sets.

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  • 2022-10-31

    Pascal's hexagon theorem reproved by elementary tools only

    Insong Choe

    Abstract : In this paper, we prove Pascal's hexagon theorem by elementary tools only. We follow the well-known route to prove the theorem by Bez\'{o}ut's theorem, explaining all the details in elementary argument. In particular, we prove a toy version of Study's lemma.

  • 2023-01-31

    Functions subordinate to the exponential function

    Priya G. Krishnan, Vaithiyanathan Ravichandran, Ponnaiah Saikrishnan

    Abstract : We use the theory of differential subordination to explore various inequalities that are satisfied by an analytic function $p$ defined on the unit disc so that the function $p$ is subordinate to the function $e^z$. These results are applied to find sufficient conditions for the normalised analytic functions $f$ defined on the unit disc to satisfy the subordination $zf'(z)/f(z) \prec e^z$.

  • 2023-04-30

    A simple proof for a result on $n$-Jordan homomorphisms

    Choonkil Park, Abbas Zivari-Kazempour

    Abstract : In this short note, we give a simple proof of the main theorem of \cite{Cheshmavar} which states that every $n$-Jordan homomorphism $h:A\longrightarrow B$ between two commutative algebras $A$ and $B$ is an $n$-homomorphism.

  • 2022-07-31

    Miao-Tam equation on almost coK"{a}hler manifolds

    Tarak Mandal

    Abstract : In the present paper, we have studied Miao-Tam equation on three dimensional almost coK"{a}hler manifolds. We have also proved that there does not exist non-trivial solution of Miao-Tam equation on the said manifolds if the dimension is greater than three. Also we give an example to verify the deduced results.

  • 2023-01-31

    Some functional identities arising from derivations

    Abdellah Mamouni, Lahcen Oukhtite, Mohammed Zerra

    Abstract : This paper considers some functional identities related to derivations of a ring $R$ and their action on the centre of $R/P$ where $P$ is a prime ideal of $R.$ It generalizes some previous results that are in the same spirit. Finally, examples proving that our restrictions cannot be relaxed are given.

  • 2023-01-31

    On the 2-absorbing submodules and zero-divisor graph of equivalence classes of zero divisors

    Shiroyeh Payrovi, Yasaman Sadatrasul

    Abstract : Let $R$ be a commutative ring, $M$ be a Noetherian $R$-module, and $N$ a 2-absorbing submodule of $M$ such that $r(N :_{R} M)= \mathfrak p$ is a prime ideal of $R$. The main result of the paper states that if $N=Q_1\cap\cdots\cap Q_n$ with $r(Q_i:_RM)=\mathfrak p_i$, for $i=1,\ldots, n$, is a minimal primary decomposition of $N$, then the following statements are true. \begin{itemize} \item[(i)] $\mathfrak p=\mathfrak p_k$ for some $1 \leq k \leq n$. \item[(ii)] For each $j=1,\ldots,n$ there exists $m_j \in M$ such that ${\mathfrak p}_j=(N :_{R} m_{j})$. \item[(iii)] For each $i,j=1,\ldots,n$ either $\mathfrak p_{i} \subseteq \mathfrak p_{j}$ or $\mathfrak p_{j} \subseteq \mathfrak p_{i}$. \end{itemize} Let $\Gamma_E(M)$ denote the zero-divisor graph of equivalence classes of zero divisors of $M$. It is shown that $\{Q_1\cap\cdots\cap Q_{n-1}, Q_1\cap\cdots\cap Q_{n-2},\ldots , Q_1\}$ is an independent subset of $V(\Gamma_E(M))$, whenever the zero submodule of $M$ is a 2-absorbing submodule and $Q_1\cap\cdots\cap Q_n=0$ is its minimal primary decomposition. Furthermore, it is proved that $\Gamma_E(M)[(0 :_{R} M)]$, the induced subgraph of $\Gamma_E(M)$ by $(0 :_{R} M)$, is complete.

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  • 2022-07-31

    Some results on the geometry of a non-conformal deformation of a metric

    Nour Elhouda Djaa, Abderrahim Zagane

    Abstract : Let $(M^{m},g)$ be an $m$-dimensional Riemannian manifold. In this paper, we introduce a new class of metric on $(M^{m},g)$, obtained by a non-conformal deformation of the metric $g$. First we investigate the Levi-Civita connection of this metric. Secondly we characterize the Riemannian curvature, the sectional curvature and the scalar curvature. In the last section we characterizes some class of proper biharmonic maps. Examples of proper biharmonic maps are constructed when $(M^{m}, g)$ is an Euclidean space.

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April, 2024
Vol.39 No.2

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