• 대한수학회논문집
• /
• 제35권4호
• /
• pp.1203-1219
• /
• 2020

Jin [7] defined a new connection on semi-Riemannian manifolds, which is a non-symmetric and non-metric connection. He said that this connection is an (ℓ, m)-type connection. Jin also studied lightlike hypersurfaces of an indefinite trans-Sasakian manifold with an (ℓ, m)-type connection in [7]. We study further the geometry of this subject. In this paper, we study generic lightlike submanifolds of an indefinite trans-Sasakian manifold endowed with an (ℓ, m)-type connection.

• Kyungpook Mathematical Journal
• /
• 제53권4호
• /
• 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.

• 호남수학학술지
• /
• 제44권2호
• /
• pp.179-194
• /
• 2022

In the present study, we investigate generic lightlike submanifolds of indefinite nearly Kaehler manifolds. After proving the existence of generic lightlike submanifolds in an indefinite generalized complex space form, a non-trivial example of this class of submanifolds is discussed. Then, we find a characterization theorem enabling the induced connection on a generic lightlike submanifold to be a metric connection. We also derive some conditions for the integrability of distributions defined on generic lightlike submanifolds. Further, we discuss the non-existence of mixed geodesic generic lightlike submanifolds in a generalized complex space form. Finally, we investigate totally umbilical generic lightlike submanifolds and minimal generic lightlike submanifolds of an indefinite nearly Kaehler manifold.

• Kyungpook Mathematical Journal
• /
• 제52권4호
• /
• pp.443-457
• /
• 2012

In this paper, we introduce screen slant lightlike submanifold of an indefinite Sasakian manifold and give examples. We prove a characterization theorem for the existence of screen slant lightlike submanifolds. We also obtain integrability conditions of both screen and radical distributions, prove characterization theorems on the existence of minimal screen slant lightlike submanifolds and give an example of proper minimal screen slant lightlike submanifolds of $R_2^9$.

• Kyungpook Mathematical Journal
• /
• 제56권2호
• /
• pp.625-638
• /
• 2016

In this paper, we introduce the notion of semi-slant lightlike submanifolds of indefinite Sasakian manifolds giving characterization theorem with some non-trivial examples of such submanifolds. Integrability conditions of distributions $D_1$, $D_2$ and RadTM on semi-slant lightlike submanifolds of an indefinite Sasakian manifold have been obtained. We also obtain necessary and sufficient conditions for foliations determined by above distributions to be totally geodesic.

• 대한수학회지
• /
• 제38권5호
• /
• pp.971-986
• /
• 2001

Equations. See Full-text.

• Kyungpook Mathematical Journal
• /
• 제50권2호
• /
• pp.267-279
• /
• 2010

In this paper, we introduce the notion of a screen slant lightlike submanifold of an indefinite Kenmotsu manifold. We provide characterization theorem for existence of screen slant lightlike submanifold with examples. Also, we give an example of a minimal screen slant lightlike submanifold of $R_2^9$ and prove some characterization theorems.

• 대한수학회보
• /
• 제60권4호
• /
• 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.

• 대한수학회지
• /
• 제60권5호
• /
• pp.1135-1136
• /
• 2023

In this erratum, we offer a correction to [J. Korean Math. Soc. 60 (2023), No. 1, pp. 115-141]. We rectify Theorem 5.7 and Table 1 of the original paper.

• 대한수학회지
• /
• 제60권1호
• /
• pp.115-141
• /
• 2023

We study a class of left-invariant pseudo-Riemannian Sasaki metrics on solvable Lie groups, which can be characterized by the property that the zero level set of the moment map relative to the action of some one-parameter subgroup {exp tX} is a normal nilpotent subgroup commuting with {exp tX}, and X is not lightlike. We characterize this geometry in terms of the Sasaki reduction and its pseudo-Kähler quotient under the action generated by the Reeb vector field. We classify pseudo-Riemannian Sasaki solvmanifolds of this type in dimension 5 and those of dimension 7 whose Kähler reduction in the above sense is abelian.