• Bulletin of the Korean Mathematical Society
• /
• v.54 no.2
• /
• pp.619-632
• /
• 2017

We define a new connection on semi-Riemannian manifold, which is called a non-metric ${\phi}$-symmetric connection. Semi-symmetric non-metric connection and quarter-symmetric non-metric connection are two impotent examples of this connection. The purpose of this paper is to study the geometry of lightlike hypersurfaces of an indefinite Kaehler manifold with a non-metric ${\phi}$-symmetric connection.

• Journal of the Korean Mathematical Society
• /
• v.41 no.3
• /
• pp.535-565
• /
• 2004

In this paper we consider the notion of ξ-invariant or (equation omitted)-invariant real hypersurfaces in a complex two-plane Grassmannian $G_2$( $C^{m+2}$) and prove that there do not exist such kinds of real hypersurfaces in $G_2$( $C^{m+2}$) with parallel second fundamental tensor on a distribution ζ defined by ζ = ξ U(equation omitted), where(equation omitted) = Span ｛ξ$_1$, ξ$_2$, ξ$_3$｝.X>｝.

• Bulletin of the Korean Mathematical Society
• /
• v.46 no.2
• /
• pp.321-329
• /
• 2009

In this paper, we have considered linear Weingarten hypersurfaces in a sphere and obtained some rigidity theorems. The purpose of this paper is to give some extension of the results due to Cheng-Yau [3] and Li [7].

• Honam Mathematical Journal
• /
• v.30 no.4
• /
• pp.743-748
• /
• 2008

In this article, we study ruled hypersurfaces in a Lorentz-Minkowski space which has finite type immersion. As a result, we give a complete classification of ruled hypersurfaces or finite type immersion into a Lorentz-Minkowski space ${\mathbb{L}}^m$.

• Communications of the Korean Mathematical Society
• /
• v.27 no.1
• /
• pp.185-195
• /
• 2012

We study the geometry of lightlike hypersurfaces M of an inde nite cosymplectic manifold $\bar{M}$ such that either (1) the characterist vector field $\zeta$ of $\bar{M}$ belongs to the screen distribution S(TM) of M or (2) $\zeta$ belongs to the orthogonal complement $S(TM)^{\perp}$ of S(TM) in $T\bar{M}$.

• Kyungpook Mathematical Journal
• /
• v.53 no.4
• /
• pp.593-602
• /
• 2013

This paper is devoted to study Ricci semi-symmetric lightlike hypersurfaces of an indefinite cosymplectic space form with structure vector field tangent to hypersurface. The condition for Ricci tensor of lightlike hypersurface of indefinite cosymplectic space form to be semi-symmetric and parallel have been obtained. An example of non-totally geodesic Ricci semi-symmetric lightlike hypersurface in $R^7_2$ have been given.

• Kyungpook Mathematical Journal
• /
• v.56 no.3
• /
• 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.

• Kyungpook Mathematical Journal
• /
• v.46 no.4
• /
• pp.463-476
• /
• 2006

It is known that there are no real hypersurfaces with parallel Ricci tensor in a nonflat complex space form ([6], [9]). In this paper we investigate real hypersurfaces in a complex projective space $P_n\mathbb{C}$ using some conditions of the Ricci tensor S which are weaker than ${\nabla}S=0$. We characterize Hopf hypersurfaces of $P_n\mathbb{C}$.

• Kyungpook Mathematical Journal
• /
• v.48 no.1
• /
• pp.109-121
• /
• 2008

We determine maximal space-like hypersurfaces which are the images of subbundles of the normal bundle of m-dimensional totally geodesic space-like submanifolds of an (m + 2)-dimensional Lorentzian space form $\tilde{M}_1^{m+2}$(c) under the normal exponential map. Then we construct examples of maximal space-like hypersurfaces of $\tilde{M}_1^{m+2}$(c).

• Communications of the Korean Mathematical Society
• /
• v.11 no.1
• /
• pp.215-224
• /
• 1996

In this paper, we classify hypersurfaces M in $S^{n+1}_{1}$ or in $H^{n+1}$ satisfying $\Delta x = Rx + b$.