• Communications of the Korean Mathematical Society
• /
• v.11 no.3
• /
• pp.757-766
• /
• 1996

The purpose of this paper is to study a real hypersurface of $M_n(c)$ where structure vector $\zeta$ is principal and satisfying $\bigtriangledown_\zeta S = (\bigtriangledown S)\zeta$ (section 2) and also satisfying $\bigtriangledown_\zeta S = a(S \phi - \phi S)$ (section 3) where a is constant.

• Bulletin of the Korean Mathematical Society
• /
• v.55 no.2
• /
• pp.515-531
• /
• 2018

Jin studied lightlike hypersurfaces of an indefinite Kaehler manifold [6, 8] or indefinite trans-Sasakian manifold [7] with a quarter-symmetric metric connection. Jin also studied generic lightlike submanifolds of an indefinite trans-Sasakian manifold with a quarter-symmetric metric connection [10]. We study generic lightlike submanifolds of an indefinite Kaehler manifold with a quarter-symmetric metric connection.

• Journal of the Chungcheong Mathematical Society
• /
• v.22 no.4
• /
• pp.653-665
• /
• 2009

We define a semi-symmetric non-metric connection in an almost r-paracontact Riemannian manifold and we consider submanifolds of an almost r-paracontact Riemannian manifold endowed with a semi-symmetric non-metric connection and obtain Gauss and Codazzi equations, Weingarten equation and curvature tensor for submanifolds of an almost r-paracontact Riemannian manifold endowed with a semi-symmetric non-metric connection.

• Journal of the Korean Data and Information Science Society
• /
• v.7 no.2
• /
• pp.203-210
• /
• 1996

A linear neural unit with a modified anti-Hebbian learning rule has been shown to be able to optimally fit curves, surfaces, and hypersurfaces by adaptively extracting the minor component of the input data set. In this paper, we study how to use the robust version of this neural fitting method for linear regression analysis. Furthermore, we compare this method with other methods when data set is contaminated by outliers.

• The Pure and Applied Mathematics
• /
• v.11 no.3
• /
• pp.197-206
• /
• 2004

We obtain some characterizations of a pseudo Ricci-parallel real hypersurface in a quaternionic projective space $QP^{n}$ and find the condition that M is locally congruent to a geodesic hypersphere of $QP^{n}$ .

• Bulletin of the Korean Mathematical Society
• /
• v.42 no.2
• /
• pp.279-294
• /
• 2005

We study a real hypersurface M satisfying $L_{\xi}S=0\;and\;R_{\xi}S=SR_{\xi}$ in a complex hyperbolic space $H_n\mathbb{C}$, where S is the Ricci tensor of type (1,1) on M, $L_{\xi}\;and\;R_{\xi}$ denotes the operator of the Lie derivative and the Jacobi operator with respect to the structure vector field e respectively.

• Journal of the Korean Mathematical Society
• /
• v.34 no.1
• /
• pp.23-42
• /
• 1997

A 6-dimensional sphere considered as a homogeneous space $G_2/SU(3)$ where $G_2$ is the group of automorphism of the octonians O. From this representation, we can define an almost comlex structure on a 6-dimensional sphere by making use of the vector cross product of the octonians. Also it is known that a homogeneous space $G_2/U(2)$ coincides with the Grassmann manifold of oriented 2-planes of a 7-dimensional Euclidean space.

• Communications of the Korean Mathematical Society
• /
• v.9 no.2
• /
• pp.369-383
• /
• 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)

• Kyungpook Mathematical Journal
• /
• v.53 no.4
• /
• pp.515-540
• /
• 2013

Let $G=O(2){\times}O(2){\times}O(2)$. Then a closed G-invariant minimal hypersurface with constant scalar curvature in $S^5$ is a product of spheres, i.e., the square norm of its second fundamental form, S = 4.

• Honam Mathematical Journal
• /
• v.28 no.3
• /
• pp.409-415
• /
• 2006

On a compact oriented smooth 3-dimensional manifold (M, g), we consider the critical point equation(CPE) defined as $z_g=s^{{\prime}*}_g(f)$. Under CPE, it is shown in [5] that every stable minimal hypersurface in M is contained in ${\varphi}^{-1}(0)$ for ${\varphi}{\in}$ ker $s^{{\prime}*}_g$. We study analytic and geometric conditions under which the stable minimal hypersurface in M does not exist.