• Communications of the Korean Mathematical Society
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• v.10 no.3
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• pp.661-679
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• 1995

The concept of the structure conformal vector field C on a Sasakian manifold M is defined. The existence of such a C on M is determined by an exterior differential system in involution. In this case M is a foliate manifold and the vector field C enjoys the property to be exterior concurrent. This allows to prove some interesting properties of the Ricci tensor and Obata's theorem concerning isometries to a sphere. Different properties of the conformal Lie algebra induced by C are also discussed.

• Journal of the Korean Mathematical Society
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• v.43 no.1
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• pp.133-145
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• 2006

We study Riemannian or pseudo-Riemannian manifolds which admit a closed conformal vector field. Subject to the condition that at each point $p{\in}M^n$ the set of conformal gradient vector fields spans a non-degenerate subspace of TpM, using a warped product structure theorem we give a complete description of the space of conformal vector fields on arbitrary non-Ricci flat Einstein spaces.

• Bulletin of the Korean Mathematical Society
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• v.59 no.1
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• pp.101-110
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• 2022

In this article, the notion of *-conformal Ricci soliton is defined as a self similar solution of the *-conformal Ricci flow. A Sasakian 3-metric satisfying the *-conformal Ricci soliton is completely classified under certain conditions on the soliton vector field. We establish a relation with Fano manifolds and proves a homothety between the Sasakian 3-metric and the Berger Sphere. Also, the potential vector field V is a harmonic infinitesimal automorphism of the contact metric structure.

• Communications of the Korean Mathematical Society
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• v.9 no.2
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• pp.393-400
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• 1994

Let M(f,η,ξ,g) be a (2m ＋ 1)-dimensional Sasakian manifold with soldering form dp ∈ ΓHom(Λ/sup q/TM, TM) (dp: canonical vector-valued 1-form) where f,η,ξ and g are the (1,1)-tensor field, the structure 1-form, the structure vector field and the metric tensor of M, respectively.(omitted)

• East Asian mathematical journal
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• v.31 no.3
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• pp.337-344
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• 2015

We study screen quasi-conformal irrotational half lightlike submanifolds M of a semi-Riemannian space form $\bar{M}$ (c) equipped with a semi-symmetric non-metric connection subject such that the structure vector field of $\bar{M}$ (c) belongs to the screen distribution S(TM). The main result is a non-existence theorem for such half lightlike submanifolds.

• The Pure and Applied Mathematics
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• v.21 no.1
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• pp.39-50
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• 2014

In this paper, we study screen quasi-conformal irrotational half lightlike submanifolds M of a semi-Riemannian space form $\tilde{M}(c)$ admitting a semi-symmetric non-metric connection, whose structure vector field ${\zeta}$ is tangent to M. The main result is a classification theorem for such Einstein half lightlike submanifolds of a Lorentzian space form admitting a semi-symmetric non-metric connection.

• Bulletin of the Korean Mathematical Society
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• v.50 no.4
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• pp.1367-1376
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• 2013

We study Einstein lightlike hypersurfaces M of a Lorentzian space form $\tilde{M}(c)$ admitting a semi-symmetric non-metric connection subject to the conditions; (1) M is screen conformal and (2) the structure vector field ${\zeta}$ of $\tilde{M}$ belongs to the screen distribution S(TM). The main result is a characterization theorem for such a lightlike hypersurface.

• Honam Mathematical Journal
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• v.35 no.3
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• pp.329-342
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• 2013

We study lightlike hypersurfaces M of a semi-Riemannian space form $\tilde{M}(c)$ with a semi-symmetric non-metric connection whose structure vector field is tangent to M. Our main result is two characterization theorems for such a lightlike hypersurface.

• Communications of the Korean Mathematical Society
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• v.28 no.4
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• pp.809-818
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• 2013

We study irrotational half lightlike submanifolds M of a semi-Riemannian space form with a semi-symmetric non-metric connection such that its structure vector field is tangent to M. We prove two characterization theorems for such an irrotational half lightlike submanifold.

• Communications of the Korean Mathematical Society
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• v.29 no.1
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• pp.109-121
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• 2014

In this paper, we study the geometry of half lightlike submanifolds of an indefinite Sasakian manifold. There are several different types of half lightlike submanifolds of an indefinite Sasakian manifold according to the form of its structure vector field. We study two types of them here: tangential and ascreen half lightlike submanifolds.