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Pyo, Yong-Soo
- Communications of the Korean Mathematical Society
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- v.9 no.2
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- pp.369-383
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- 1994
A complex n-dimensional Kahler manifold of constant holomorphic sectional curvature c is called a complex space form, which is denoted by $M_{n}$ (c). A complete and simply connected complex space form consists of a complex projective space $P_{n}$ C, a complex Euclidean space $C^{n}$ or a complex hyperbolic space $H_{n}$ C, according as c > 0, c = 0 or c < 0.(omitted)
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Kwon, Jung-Hwan;Nakagawa, Hisao
- Bulletin of the Korean Mathematical Society
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- v.26 no.1
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- pp.75-82
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- 1989
It is recently proved by Aiyama and the authors [2] that a complete space-like complex submanifold of a complex space form $M^{n+p}$$_{p}$ (c') (c'.geq.0) is to totally geodesic. This is a complex version of the Bernstein-type theorem in the Minkowski space due to Calabi [4] and Cheng and Yau [5], which is generalized by Nishikawa[7] in the Lorentz manifold satisfying the strong energy condition. The purpose of this paper is to consider his result in the complex Lorentz manifold and is to prove the following.e following.
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Jee, Seo-In;Lee, Jae-Hyouk
- The Pure and Applied Mathematics
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- v.21 no.4
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- pp.257-270
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- 2014
In this article, we consider a homogeneous function of degree four in quaternionic vector spaces and $S^{4n+3}$ which is invariant under $S^3$ and U(n + 1)-action. We show it is an isoparametric function providing isoparametric hypersurfaces in $S^{4n+3}$ with g = 4 distinct principal curvatures and isoparametric hypersurfaces in quaternionic projective spaces with g = 5. This extends study of Nomizu on isoparametric function on complex vector spaces and complex projective spaces.
https://doi.org/10.7468/jksmeb.2014.21.4.257 인용 PDF KSCI KPUBS HTML

Ki, U-Hang;Kim, In-Bae;Lim, Dong-Ho
- Bulletin of the Korean Mathematical Society
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- v.47 no.1
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- pp.1-15
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- 2010
Let M be a real hypersurface with almost contact metric structure $(\phi,g,\xi,\eta)$ in a complex space form $M_n(c)$, $c\neq0$. In this paper we prove that if $R_{\xi}L_{\xi}g=0$ holds on M, then M is a Hopf hypersurface in $M_n(c)$, where $R_{\xi}$ and $L_{\xi}$ denote the structure Jacobi operator and the operator of the Lie derivative with respect to the structure vector field $\xi$ respectively. We characterize such Hopf hypersurfaces of $M_n(c)$.
https://doi.org/10.4134/BKMS.2010.47.1.001 인용 PDF KSCI