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On Some Ruled Real Hypersurfaces in a Complex Space Form
Kim,Hyang Sook 인제대학교기초과학연구소 1998 자연과학 Vol.2 No.-
상수인 단면곡률(sectional curvature) c를 계량(metric)으로 가지는 n차원 복소공간형(complex space form) Mn(c)는 c>0일 때 Pn(C), c>0일 때 Cⁿ이 된다. 복소공간형의 균질(homogeneous) 실초곡면(real hypersurface)은 R. Takagi와 J.Berndt에 의해 각 각 1973년, 1989년에 분류되어졌다. 그 후로 많은 기하학자들이 분류되어진 각 모형(model)을 특성(characterization) 지우는 문제에 관심을 가지게 되었다. 또, 1987년 M. Kimura는 직선(ruled) 실초곡면을 정의하고, 그 이후로 이 곡면에 대해 괄목할 만한 결과들을 내 놓았다. 본 논문은 직선 실초곡면을 일반화시킨 의사-측지적 (pesudo-geodesic) 직선 실초곡면을 정의하고 그에 관한 특성을 연구하였으며, 특히 의사-측지적 직선 실초곡면이 어떤 조건하에서 M. Kimura가 정의한 실초곡면이 될 수 있는 지를 조사하였다. We denote by Mn(c) a complex space form with the metric of constant holomorphic sectional curvature c. In this paper, we define a pseudo-geodesic ruled real hypersurface in Mn(c), c≠0 and investigated some characterizations of this kind of real hypersurfaces.
A NEW CHARACTERIZATION OF RULED REAL HYPERSURFACES IN COMPLEX SPACE FORMS
Ahn, Seong-Soo,Choi, Young-Suk,Suh, Young-Jin Korean Mathematical Society 1999 대한수학회보 Vol.36 No.3
The purpose of this paper is to give another new characterization of ruled real hypersurfaces in a complex space form $M_n$(c), c$\neq$0 in terms of the covariant derivative of its Weingarten map in the direction of the structure vector $\xi$.
A new characterization of type $(A)$ and ruled real hypersurfaces in nonflat complex space forms
Yaning Wang 대한수학회 2022 대한수학회보 Vol.59 No.4
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 $(A)$.
Ricci solitons of compact real hypersurfaces in Kähler manifolds
Cho, Jong Taek,Kimura, Makoto WILEY‐VCH Verlag 2011 Mathematische Nachrichten Vol.284 No.11
<P><B>Abstract</B></P><P>If a compact real hypersurface of contact‐type in a complex number space admits a Ricci soliton, then it is a sphere. A compact Hopf hypersurface in a non‐flat complex space form does not admit a Ricci soliton. © 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim</P>
ON NON-PROPER PSEUDO-EINSTEIN RULED REAL HYPERSURFACES IN COMPLEX SPACE FORMS
Suh, Young-Jin Korean Mathematical Society 1999 대한수학회보 Vol.36 No.2
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.