Journal of the
Korean Mathematical Society

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

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The following are papers that have received final approval and are awaiting to be published. They are listed in the order of their initial submission date.
Papers are published in the order of their initial submission date and will be made available under “Current Issue” once scheduled to be included in a print issue.

Note: Please understand the below list is not in the exact publishing order of the papers as the list does not include papers under internal reviewing process nor those that have not been galley proofed by the authors.

Final published versions of all papers are available under “All Issues” and also under “Current Issue” for papers included in the current issue.

* Paper information have been automatically generated from the information submitted by authors in the online submission system.
  • Online first article September 1, 2023

    Real hypersurfaces in the complex hyperbolic quadric with cyclic parallel structure Jacobi operator

    Jin Hong Kim, Hyunjin Lee, and Young Jin Suh

    Abstract : Let $M$ be a real hypersurface in the complex hyperbolic quadric ${Q^{m}}^{*}$, $m \geq 3$. The Riemannian curvature tensor field $R$ of $M$ allows us to define a symmetric Jacobi operator with respect to the Reeb vector field $\xi$, which is called the structure Jacobi operator $R_{\xi} = R(\, \cdot \, , \xi) \xi \in \mathrm{End}(TM)$. On the other hand, in [Math. Z. 245 (2003), 503-527], Semmelmann showed that the cyclic parallelism is equivalent to the Killing property regarding any symmetric tensor. Motivated by his result above, in this paper we consider the cyclic parallelism of the structure Jacobi operator $R_{\xi}$ for a real hypersurface $M$ in the complex hyperbolic quadric ${Q^{m}}^{*}$. Furthermore, we give a complete classification of Hopf real hypersurfaces in ${Q^{m}}^{*}$ with such a property.

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  • Online first article August 30, 2023

    Existence of solutions to a generalized self-dual Chern-Simons equation on finite graphs

    Yuanyang Hu

    Abstract : Let $G=(V,E)$ be a connected finite graph. We study the existence of solutions for the following generalized Chern-Simons equation on $G$ \begin{equation*} \Delta u=\lambda \mathrm{e}^{u}\left(\mathrm{e}^{u}-1\right)^{5}+4 \pi \sum_{s=1}^{N} \delta_{p_{s}}~, \end{equation*} where $\lambda>0$, $\delta_{p_{s}}$ is the Dirac mass at the vetex $p_s$, and $p_1, p_2,\dots, p_N$ are arbitrarily chosen distinct vertices on the graph. We show that there exists a critial value $\hat{\lambda}$ such that when $\lambda > \hat{\lambda}$, the generalized Chern-Simons equation has at least two solutions, when $\lambda = \hat{\lambda}$, the generalized Chern-Simons equation has a solution, and when $\lambda < \hat\lambda$, the generalized Chern-Simons equation has no solution.

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  • Online first article October 20, 2023

    An intrinsic proof of Numata’s theorem on Landsberg spaces

    Salah Gomaa Elgendi and Amr Soleiman

    Abstract : In this paper, we study the unicorn’s Landsberg problem from an intrinsic point of view. Precisely, we investigate a coordinate-free proof of Numata’s theorem on Landsberg spaces of scalar curvature. In other words, following the pullback approach to Finsler geometry, we prove that all Landsberg spaces of dimension n ≥ 3 of non-zero scalar curvature are Riemannian spaces of constant curvature

  • Online first article October 23, 2023

    Complete noncompact submanifolds of manifolds with negative curvature

    Ya Gao, Yanling Gao, Jing Mao, and Zhiqi Xie

    Abstract : In this paper, for a $m$-dimensional ($m\geq5$) complete noncompact submanifold $M$ immersed in an $n$-dimensional ($n\geq6$) simply connected Riemannian manifold $N$ with negative sectional curvature, under suitable constraints on the squared norm of the second fundamental form of $M$, the norm of its weighted mean curvature vector $|\textbf{H}_{f}|$ and the weighted real-valued function $f$, we can obtain: several one-end theorems for $M$; two Liouville theorems for harmonic maps from $M$ to complete Riemannian manifolds with nonpositive sectional curvature.

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November, 2023
Vol.60 No.6

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