• Bulletin of the Korean Mathematical Society
• /
• v.50 no.6
• /
• pp.2089-2101
• /
• 2013

The aim of this paper is to introduce the notion of Lie recurrent structure Jacobi operator for real hypersurfaces in non-flat complex space forms and to study such real hypersurfaces. More precisely, the non-existence of such real hypersurfaces is proved.

• Communications of the Korean Mathematical Society
• /
• v.25 no.2
• /
• pp.225-234
• /
• 2010

In this paper, we study the geometry of lightlike hypersurfaces of a semi-Riemannian manifold. We prove a classification theorem for Einstein lightlike hypersurfaces M of a Lorentzian space form subject such that the second fundamental forms of M and its screen distribution S(TM) are conformally related by some non-vanishing smooth function.

• Bulletin of the Korean Mathematical Society
• /
• v.40 no.1
• /
• pp.63-76
• /
• 2003

In this article, we establish relations between the sectional curvature and the shape operator and also between the k-Ricci curvature and the shape operator for a slant submanifold in a Sasakian space form of constant $\varphi-sectional$ curvature with arbitrary codimension.

• Bulletin of the Korean Mathematical Society
• /
• v.36 no.2
• /
• pp.315-336
• /
• 1999

In the paper [12] we have introduced the new kind of pseudo-einstein ruled real hypersurfaces in complex space forms $M_n(c), c\neq0$, which are foliated by pseudo-Einstein leaves. The purpose of this paper is to give a geometric condition for non-proper pseudo-Einstein ruled real hypersurfaces to be totally geodesic in the sense of Kimura [8] for c> and Ahn, Lee and the present author [1] for c<0.

• Bulletin of the Korean Mathematical Society
• /
• v.59 no.4
• /
• pp.897-904
• /
• 2022

In this paper, we obtain an inequality involving the squared norm of the covariant differentiation of the shape operator for a real hypersurface in nonflat complex space forms. It is proved that the equality holds for non-Hopf case if and only if the hypersurface is ruled and the equality holds for Hopf case if and only if the hypersurface is of type (A).

• Kyungpook Mathematical Journal
• /
• v.31 no.2
• /
• pp.131-141
• /
• 1991

• Journal of the Korean Mathematical Society
• /
• v.55 no.3
• /
• pp.735-747
• /
• 2018

Let M be a real hypersurface of a complex space form with constant curvature c. In this paper, we study the hypersurface M admitting Miao-Tam critical metric, i.e., the induced metric g on M satisfies the equation: $-({\Delta}_g{\lambda})g+{\nabla}^2_g{\lambda}-{\lambda}Ric=g$, where ${\lambda}$ is a smooth function on M. At first, for the case where M is Hopf, c = 0 and $c{\neq}0$ are considered respectively. For the non-Hopf case, we prove that the ruled real hypersurfaces of non-flat complex space forms do not admit Miao-Tam critical metrics. Finally, it is proved that a compact hypersurface of a complex Euclidean space admitting Miao-Tam critical metric with ${\lambda}$ > 0 or ${\lambda}$ < 0 is a sphere and a compact hypersurface of a non-flat complex space form does not exist such a critical metric.

• Bulletin of the Korean Mathematical Society
• /
• v.54 no.2
• /
• pp.417-428
• /
• 2017

We classify the extreme bilinear forms of the unit ball of the space of bilinear forms on ${\mathbb{R}}^2$ with hexagonal norms.

• Kyungpook Mathematical Journal
• /
• v.58 no.1
• /
• pp.47-54
• /
• 2018

We classify the extreme, exposed and smooth bilinear forms of the unit ball of the space of bilinear forms on $l^2_{\infty}$.

• Kyungpook Mathematical Journal
• /
• v.54 no.3
• /
• pp.341-347
• /
• 2014

We classify the exposed symmetric bilinear forms of the unit ball of $\mathcal{L}_s(^2d_*(1,{\omega})^2)$.