• Bulletin of the Korean Mathematical Society
• /
• v.60 no.4
• /
• pp.1003-1016
• /
• 2023

In this paper, we introduce the idea of twisted product lightlike submanifolds of semi-Riemannian manifolds and provide non-trivial examples of such lightlike submanifolds. Then, we prove the non-existence of proper isotropic or totally lightlike twisted product submanifolds of a semi-Riemannian manifold. We also show that for a twisted product lightlike submanifold of a semi-Riemannian manifold, the induced connection ∇ is not a metric connection. Further, we prove that a totally umbilical SCR-lightlike submanifold of an indefinite Kaehler manifold ${\tilde{M}}$ does not admit any twisted product SCR-lightlike submanifold of the type M_⊥×_ϕM_T, where M_⊥ is a totally real submanifold and MT is a holomorphic submanifold of ${\tilde{M}}$. Consequently, we obtain a geometric inequality for the second fundamental form of twisted product SCR-lightlike submanifolds of the type M_T×_ϕM_⊥ of an indefinite Kaehler manifold ${\tilde{M}}$, in terms of the gradient of ln ϕ, where ϕ stands for the twisting function. Subsequently, the equality case of this inequality is discussed. Finally, we construct a non-trivial example of a twisted product SCR-lightlike submanifold in an indefinite Kaehler manifold.

• Honam Mathematical Journal
• /
• v.45 no.4
• /
• pp.629-647
• /
• 2023

We introduce the study of a new class of a lightlike submersion d. Then, we derive a relationship between the holomorphic section 𝜙 : K₁ → K' from a screen generic lightlike submanifold of an indefinite Kaehler manifold K₂ onto an indefinite almost Hermitian manifold K', and show that for this case K' must be an indefinite Kaehler manifold. Then, we derive a relationship between the holomorphic sectional curvatures of K₂ and K'. Finally, we present a classification theorem for a screen generic lightlike submersion, giving the relationship between the sectional curvatures of the total space K₂ and the fibers.

• Communications of the Korean Mathematical Society
• /
• v.26 no.4
• /
• pp.635-647
• /
• 2011

In this paper, we study the geometry of real half lightlike submanifolds of an indefinite Kaehler manifold $\bar{M}$. We provide several new results on such a real half lightlike submanifold M by using the F-structure of M induced by the almost complex structure J of $\bar{M}$.

• Honam Mathematical Journal
• /
• v.43 no.2
• /
• pp.239-258
• /
• 2021

In the present paper, we introduce the study of slant lightlike submanifolds of indefinite nearly Kaehler manifolds. After proving some geometric results for the existence of slant lightlike submanifolds of indefinite nearly Kaehler manifolds, we give a non-trivial example of this class of lightlike submanifolds. Then, we derive some conditions for the integrability of the distributions associated with slant lightlike submanifolds of indefinite nearly Kaehler manifolds. Consequently, we study totally umbilical slant lightlike submanifolds of indefinite nearly Kaehler manifolds. Subsequently, we investigate minimal slant lightlike submanifolds of indefinite nearly Kaehler manifolds.

• Bulletin of the Korean Mathematical Society
• /
• v.52 no.1
• /
• pp.201-213
• /
• 2015

In this paper, we study lightlike hypersurfaces of an indefinite Kaehler manifold with a quarter-symmetric metric connection. We prove several classification theorems for such a lightlike hypersurface.

• Honam Mathematical Journal
• /
• v.36 no.2
• /
• pp.217-232
• /
• 2014

In this paper, we study the geometry of half lightlike submanifolds of an indefinite Kaehler manifold equipped with a quarter-symmetric metric connection. The main result is to prove several classification theorems for such half lightlike submanifolds.

• 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.

• East Asian mathematical journal
• /
• v.32 no.1
• /
• pp.1-11
• /
• 2016

We study transversal half lightlike submanifolds of an indefinite Kaehler manifold of a quasi-constant curvature. First, we provide a new result for such a transversal half lightlike submanifold. Next, we investigate a statical half lightlike submanifold M such that (1) the screen distribution S(TM) is totally umbilical, or (2) M is screen homothetic.

• Bulletin of the Korean Mathematical Society
• /
• v.53 no.4
• /
• pp.1171-1184
• /
• 2016

We define a new connection on semi-Riemannian manifolds, which is called a symmetric connection of type (${\ell}$, m). Semi-symmetric connection and quarter-symmetric connection are two examples of this connection such that $({\ell},m)=(1,0)$ and $({\ell},m)=(0,1)$ respectively. In this paper, we study lightlike hypersurfaces of an indefinite Kaehler manifold endowed with a symmetric metric connection of type (${\ell}$, m).

• Communications of the Korean Mathematical Society
• /
• v.31 no.2
• /
• pp.365-377
• /
• 2016

In this paper, we study half lightlike submanifolds M of an indefinite Kaehler manifold $\bar{M}$ of quasi-constant curvature such that the characteristic vector field ${\zeta}$ of $\bar{M}$ is tangent to M. First, we provide a new result for such a half lightlike submanifold. Next, we investigate a statical half lightlike submanifold M of $\bar{M}$ subject such that (1) the screen distribution S(TM) is totally umbilical or (2) M is screen conformal.