• 대한수학회보
• /
• 제41권4호
• /
• pp.609-618
• /
• 2004

Pseudo-parallel real hypersurfaces in complex space forms can be defined as an extrinsic analogues of pseudo-symmetric real hypersurfaces, that generalize the notion of semi-symmetric real hypersurface. In this paper a classification of the pseudo-parallel real hypersurfaces in a non-flat complex space forms is obtained.

• Kyungpook Mathematical Journal
• /
• 제56권3호
• /
• pp.993-1002
• /
• 2016

In this paper we give some non-existence theorems for parallel normal Jacobi operator of real hypersurfaces in real, complex and quaternionic space forms, respectively.

• 대한수학회보
• /
• 제50권6호
• /
• 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.

• 대한수학회보
• /
• 제34권3호
• /
• pp.459-468
• /
• 1997

The purpose of this paper is to give some characterizations of homogeneous real hypersurfaces of type A in complex space forms $M_n(c), c \neq 0$, in terms of Lie derivatives.

• 대한수학회논문집
• /
• 제16권2호
• /
• pp.253-263
• /
• 2001

Niebergall and Ryan posed some open questions on 3-dimensional real hypersurfaces in complex space forms. In this paper we give affirmative answers to such kind of questions.

• 대한수학회보
• /
• 제36권2호
• /
• 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.

• 대한수학회보
• /
• 제41권4호
• /
• pp.699-708
• /
• 2004

Niebergall and Ryan posed many open problems on real hypersurfaces in complex space forms. One of them is "Are there any Ricci-parallel real hypersurfaces in complex projective space $P_2C$ or complex hyperbolic space $H_2C$\ulcorner" The purpose of present paper is to prove the nonexistence of such hypersurfaces.

• 대한수학회보
• /
• 제44권1호
• /
• pp.195-202
• /
• 2007

We prove that a real hypersurface M in a complex space form Mn(c), $c{\neq}0$, whose Ricci operator and structure tensor commute each other on the holomorphic distribution and the Ricci operator is ${\eta}-parallel$, is a Hopf hypersurface. We also give a characterization of this hypersurface.

• 호남수학학술지
• /
• 제32권4호
• /
• pp.747-761
• /
• 2010

It is known that there are no real hypersurfaces with parallel structure Jacobi operator $R_{\xi}$ (cf.[16], [17]). In this paper we investigate real hypersurfaces in a nonflat complex space form using some conditions of the structure Jacobi operator $R_{\xi}$ which are weaker than ${\nabla}R_{\xi}$ = 0. Under further condition $S\phi={\phi}S$ for the Ricci tensor S we characterize Hopf hypersurfaces in a complex space form.

• 대한수학회지
• /
• 제55권3호
• /
• 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.