• Communications of the Korean Mathematical Society
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• v.28 no.2
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• pp.353-360
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• 2013

We study lightlike hypersurfaces of indefinite Kenmotsu manifolds. The purpose of this paper is to prove that there do not exist totally geodesic screen distributions on semi-symmetric lightlike hypersurfaces of indefinite Kenmotsu manifolds with flat transversal connection.

• Communications of the Korean Mathematical Society
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• v.29 no.2
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• pp.311-317
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• 2014

We study lightlike hypersurfaces of a semi-Riemannian space form $\tilde{M}(c)$ admitting a semi-symmetric non-metric connection. First, we construct a type of lightlike hypersurfaces according to the form of the structure vector field of $\tilde{M}(c)$, which is called a ascreen lightlike hypersurface. Next, we prove a characterization theorem for such an ascreen lightlike hypersurface endow with a totally geodesic screen distribution.

• 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.

• Journal of the Korean Mathematical Society
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• v.45 no.2
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• pp.493-511
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• 2008

In this article, we study the relations of horizontally homothetic harmonic morphisms with the stability of totally geodesic submanifolds. Let $\varphi:(M^n,g)\rightarrow(N^m,h)$ be a horizontally homothetic harmonic morphism from a Riemannian manifold into a Riemannian manifold of non-positive sectional curvature and let T be the tensor measuring minimality or totally geodesics of fibers of $\varphi$. We prove that if T is parallel and the horizontal distribution is integrable, then for any totally geodesic submanifold P in N, the inverse set, $\varphi^{-1}$(P), is volume-stable in M. In case that P is a totally geodesic hypersurface the condition on the curvature can be weakened to Ricci curvature.

• Honam Mathematical Journal
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• v.40 no.3
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• pp.521-528
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• 2018

The object of the present paper is to study a decomposable $(APS)_n$ and hypersurfaces of $(APS)_n$. Also, the existence of a decomposable $(APS)_n$ is ensured by a proper example.

• 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 $\tilde{M}$.

• East Asian mathematical journal
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• v.31 no.1
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• pp.27-32
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• 2015

In this paper, we study lightlike hypersurfaces M of a Lorentz manifold $\bar{M}$ with a semi-symmetric non-metric connection subject to the conditions; (1) the screen distribution S(TM) is totally geodesic in M, and (2) the second fundamental form B of M is parallel.

• Bulletin of the Korean Mathematical Society
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• v.36 no.2
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• pp.315-336
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• 1999

In the paper [12] we have introduced the new kind of pseudo-einstein ruled real hypersurfaces in complex space forms $M_n(c), c\neq0$, which are foliated by pseudo-Einstein leaves. The purpose of this paper is to give a geometric condition for non-proper pseudo-Einstein ruled real hypersurfaces to be totally geodesic in the sense of Kimura [8] for c> and Ahn, Lee and the present author [1] for c<0.

• 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.

• The Pure and Applied Mathematics
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• v.20 no.1
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• pp.25-35
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• 2013

In this paper, we study lightlike hypersurfaces of an indefinite Sasakian manifold $\bar{M}$. First, we construct a type of lightlike hypersurface according to the form of the structure vector field of $\bar{M}$, named by ascreen lightlike hypersurface. Next, we characterize the geometry of such ascreen lightlike hypersurfaces.