• Kyungpook Mathematical Journal
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• v.57 no.3
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• pp.503-516
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• 2017

In this paper, we study totally umbilical slant lightlike submanifolds of indefinite Kaehler manifolds. We prove that there do not exist totally umbilical proper slant lightlike submanifolds in indefinite Kaehler manifolds other than totally geodesic proper slant lightlike submanifolds. We also prove that there do not exist totally umbilical proper slant lightlike submanifolds of indefinite Kaehler space forms. Finally, we give a characterization theorem on minimal slant lightlike submanifolds.

• Communications of the Korean Mathematical Society
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• v.27 no.4
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• pp.763-770
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• 2012

In this paper, we study the geometry lightlike hypersurfaces (M, $g$, S(TM)) of a semi-Riemannian manifold ($\tilde{M}$, $\tilde{g}$) of quasi-constant curvature subject to the conditions: (1) The curvature vector field of $\tilde{M}$ is tangent to M, and (2) the screen distribution S(TM) is either totally geodesic in M or totally umbilical in $\tilde{M}$.

• The Pure and Applied Mathematics
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• v.17 no.1
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• pp.29-38
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• 2010

We study the geometry of half light like submanifold M of a semi-Riemannian space form $\bar{M}$(c) subject to the conditions : (a) the screen distribution on M is totally umbilic in M and the coscreen distribution on M is conformal Killing on $\bar{M}$ or (b) the screen distribution is totally geodesic in M and M is irrotational.

• Nonlinear Functional Analysis and Applications
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• v.26 no.5
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• pp.985-994
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• 2021

The object of this paper is to study non-invariant hypersurface of a (𝜖, 𝛿)-trans Sasakian manifolds equipped with (f, g, u, v, λ)-structure. Some properties obeyed by this structure are obtained. The necessary and sufficient conditions also have been obtained for totally umbilical non-invariant hypersurface with (f, g, u, v, λ)-structure of a (𝜖, 𝛿)-trans Sasakian manifolds to be totally geodesic. The second fundamental form of a non-invariant hypersurface of a (𝜖, 𝛿)-trans Sasakian manifolds with (f, g, u, v, λ)-structure has been traced under the condition when f is parallel.

• Honam Mathematical Journal
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• v.46 no.3
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• pp.452-472
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• 2024

We introduce the study of a semi-slant lightlike submersion from an indefinite Kaehler manifold onto an r-lightlike manifold. After giving the definition of a semi-slant lightlike submersion, we establish the existence Theorems for this class of lightlike submersions. Then, we derive the integrability conditions for the distributions D₁, D₂ and ∆ associated with a semi-slant lightlike submersion. Consequently, we find some necessary and sufficient conditions for the foliations determined by the distributions D₁, D₂ and ∆. Subsequently, we examine the geometry of totally umbilical fibres of a semi-slant lightlike submersion.

• Communications of the Korean Mathematical Society
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• v.33 no.4
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• pp.1331-1339
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• 2018

In this paper the decomposition of basic equations of $(LCS)_n$-manifolds is carried out into horizontal and vertical projections. Further, we study the integrability of the distributions $D,D{\oplus}[{\xi}]$ and $D^{\perp}$ totally geodesic of semi-invariant submanifolds of $(LCS)_n$-manifold.

• Honam Mathematical Journal
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• v.42 no.1
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• pp.123-137
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• 2020

The object of the present paper is to study certain geometrical properties of the submanifolds of generalized Sasakian space-forms. We deduce some results related to the invariant and anti-invariant slant submanifolds of the generalized Sasakian spaceforms. Finally, we study the properties of the sectional curvature, totally geodesic and umbilical submanifolds of the generalized Sasakian space-forms. To prove the existence of almost semiinvariant and anti-invariant submanifolds, we provide the non-trivial examples.

• Journal of the Chungcheong Mathematical Society
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• v.24 no.4
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• pp.769-781
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• 2011

We study the geometry of half lightlike sbmanifolds M of a semi-Riemannian space form $\tilde{M}(c)$ admitting a semi-symmetric metric connection subject to the conditions: (1) The screen distribution S(TM) is totally umbilical (geodesic) and (2) the co-screen distribution $S(TM^{\bot})$ of M is a conformal Killing one.

• Communications of the Korean Mathematical Society
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• v.38 no.1
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• pp.223-234
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• 2023

The main purpose of this paper is to study the lightlike hypersurface (M, $\overline{g}$) of cosymplectic space form $\overline{M}$(c). In this paper, we computed the Gauss and Codazzi formulae of (M, $\overline{g}$) of cosymplectic manifold ($\overline{M}$, g). We showed that we can't obtain screen semi-invariant lightlike hypersurface (SCI-LH) of $\overline{M}$(c) with parallel second fundamental form h, parallel screen distribution and c ≠ 0. We showed that if second fundamental form h and local second fundamental form B are parallel, then (M, $\overline{g}$) is totally geodesic. Finally we showed that if (M, $\overline{g}$) is umbilical, then cosymplectic manifold ($\overline{M}$, g) is flat.

• Communications of the Korean Mathematical Society
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• v.36 no.2
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• pp.361-375
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• 2021

The object of the present paper is to deduce some important results on generic submanifolds and also generic product of LP-Sasakian manifolds with concurrent vector fields. Also, we provide a necessary and sufficient condition for which the invariant distribution D and anti-invariant distribution D^⊥ of M are Einstein. Also, we deduce an interesting necessary and sufficient condition for submanifolds of LP-Sasakian manifolds to be totally umbilical submanifolds. Especially we deal with the generic submanifolds admitting a Ricci soliton in LP-Sasakian manifolds endowed with concurrent vector fields.