• Communications of the Korean Mathematical Society
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• v.29 no.4
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• pp.569-579
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• 2014

We consider a condition under which the projectivization $P(E^k)$ of a complex k-bundle $E^k{\rightarrow}M$ over an even-dimensional manifold M can have the hard Lefschetz property, affected by [10]. It depends strongly on the rank k of the bundle $E^k$. Our approach is purely algebraic by using rational Sullivan minimal models [5]. We will give some examples.

• Bulletin of the Korean Mathematical Society
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• v.50 no.4
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• pp.1099-1108
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• 2013

We define the Mannheim curve in a 3-dimensional Riemannian manifold, which is a generalization of the Mannheim curve in Euclidean space. In particular, we study the Mannheim curves and their partner curves in 3-dimensional space forms.

• 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.

• Bulletin of the Korean Mathematical Society
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• v.38 no.3
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• pp.551-564
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• 2001

We view Weyl structures as generalizations of Riemannian metrics and study the critical points of geometric functional which involve scalar curvature, defined on the space of Weyl structures on a closed 4-manifold. The main goal here is to provide a framework to analyze critical Weyl structures by defining functionals, discussing function spaces and writing down basic formulas for the equations of critical points.

• Bulletin of the Korean Mathematical Society
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• v.39 no.4
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• pp.681-685
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• 2002

It is shown that, an immersion of n-dimensional compact manifold without boundary into (n + 1)-dimensional Euclidean space, hyperbolic space or the open half spheres, is a totally umbilic immersion if for some r, r =2, 3, …, n the r-th mean curvature Hr does not vanish and there are nonnegative constants $C_1$, $C_2$, …, $C_{r}$ such that (equation omitted)d)

• Kyungpook Mathematical Journal
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• v.55 no.4
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• pp.1097-1104
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• 2015

In this paper, we study the geometry of indefinite generalized Sasakian space form $\bar{M}(f_1,f_2,f_3)$ admitting a lightlike hypersurface M subject such that the almost contact structure vector field ${\zeta}$ of $\bar{M}(f_1,f_2,f_3)$ is tangent to M. We prove a classification theorem of such an indefinite generalized Sasakian space form.

• Honam Mathematical Journal
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• v.41 no.4
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• pp.707-724
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• 2019

We investigate the new Clairaut conditions for anti-invariant submersions whose total manifolds are cosymplectic. In particular, we prove the fibers of a proper Clairaut Lagrangian submersion admitting horizontal Reeb vector field are one dimensional and classify such submersions. We also check the existence of the proper Clairaut anti-invariant submersions in the case of the Reeb vector field is vertical. Moreover, illustrative examples for both trivial and proper Clairaut anti-invariant submersions are given.

• Journal of the Chungcheong Mathematical Society
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• v.28 no.4
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• pp.591-602
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• 2015

In this paper, we prove the existence and the nonexistence of warping functions on Riemannian warped product manifolds with some prescribed scalar curvatures according to the fiber manifolds of class (A).

• Korean Journal of Mathematics
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• v.19 no.4
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• pp.381-390
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• 2011

This paper is a direct continuation of [1]. In this paper we derive tensorial representations of contracted ES curvature tensors of $g-ESX_n$ and prove several generalized identities involving them. In particular, a variation of the generalized Bianchi's identity in $g-ESX_n$, which has a great deal of useful physical applications, is proved in Theorem (2.9).

• Korean Journal of Mathematics
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• v.22 no.4
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• pp.621-632
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• 2014

In this paper, we study the dynamical behavior of the one-dimensional convective Cahn-Hilliard equation(CCHE) on a periodic cell [$-{\pi},{\pi}$]. We prove that as the control parameter passes through the critical number, the CCHE bifurcates from the trivial solution to an attractor. We describe the bifurcated attractor in detail which gives the final patterns of solutions near the trivial solution.