• Bulletin of the Korean Mathematical Society
• /
• v.49 no.6
• /
• pp.1163-1178
• /
• 2012

In this paper, we study the geometry of Einstein half lightlike submanifolds M of a semi-Riemannian space form $\bar{M}(c)$ subject to the conditions: (a) M is screen conformal, and (b) the coscreen distribution of M is a conformal Killing one. The main result is a classification theorem for screen conformal Einstein half lightlike submanifolds of a Lorentzian space form with a conformal Killing coscreen distribution.

• The Pure and Applied Mathematics
• /
• v.10 no.2
• /
• pp.71-102
• /
• 2003

The purpose of this paper is to study the geometry of null curves in a 6-dimensional semi-Riemannian manifold $M_q$ of index q, since the general n-dimensional cases are too complicated. We show that it is possible to construct three types of Frenet equations of null curves in $M_q$, supported by one example. We find each types of Frenet equations invariant under any causal change. And we discuss some properties of null curves in $M_q$.

• Communications of the Korean Mathematical Society
• /
• v.33 no.1
• /
• pp.273-291
• /
• 2018

In this paper we investigate the geometry of doubly twisted product manifolds and we study the harmonicity and biharmonicity of maps between doubly twisted product Riemannian manifold. Also we characterize the conformal biharmonic maps and construct some new proper biharmonic maps.

• Honam Mathematical Journal
• /
• v.43 no.1
• /
• pp.152-166
• /
• 2021

In this paper, we study the geometry of semi-slant lightlike submanifolds of an indefinite Kenmotsu manifold. The integrability conditions of distributions D1 ⊕ {V}, D2 ⊕ {V} and RadTM on semi-slant lightlike submanifolds of an indefinite Kenmotsu manifold are defined. Furthermore, we derive necessary and sufficient conditions for the above distributions to have totally geodesic foliations.

• Kyungpook Mathematical Journal
• /
• v.46 no.3
• /
• pp.367-376
• /
• 2006

We investigate semi-symmetry and pseudo-symmetry of some 3-dimensional Riemannian manifolds: the D'Atri spaces, the Thurston geometries as well as the ${\eta}$-Einstein manifolds. We prove that all these manifolds are pseudo-symmetric and that many of them are not semi-symmetric.

• 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.

• Communications of the Korean Mathematical Society
• /
• v.25 no.2
• /
• pp.225-234
• /
• 2010

In this paper, we study the geometry of lightlike hypersurfaces of a semi-Riemannian manifold. We prove a classification theorem for Einstein lightlike hypersurfaces M of a Lorentzian space form subject such that the second fundamental forms of M and its screen distribution S(TM) are conformally related by some non-vanishing smooth function.

• Honam Mathematical Journal
• /
• v.30 no.3
• /
• pp.487-504
• /
• 2008

In this paper we study the geometry of codimension 2 screen conformal Einstein half lightiike submanifolds M of a semi-Riemannian manifold $(\={M}(c),\={g})$ of constant curvature c, with a Killing co-screen distribution on $\={M}$. The main result is a classification theorem for screen homothetic Einstein half lightlike submanifold of Lorentzian space forms.

• Journal of the Korean Mathematical Society
• /
• v.61 no.1
• /
• pp.149-160
• /
• 2024

In this paper, we study the unicorn's Landsberg problem from an intrinsic point of view. Precisely, we investigate a coordinate-free proof of Numata's theorem on Landsberg spaces of scalar curvature. In other words, following the pullback approach to Finsler geometry, we prove that all Landsberg spaces of dimension n ≥ 3 of non-zero scalar curvature are Riemannian spaces of constant curvature.

• Communications of the Korean Mathematical Society
• /
• v.31 no.3
• /
• pp.613-624
• /
• 2016

We define a new connection on a semi-Riemannian manifold. Its notion contains two well known notions; (1) semi-symmetric connection and (2) quarter-symmetric connection. In this paper, we study the geometry of lightlike hypersurfaces of an indefinite generalized Sasakian space form with a symmetric metric connection of type (${\ell}$, m).