• Kyungpook Mathematical Journal
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• v.50 no.2
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• pp.337-343
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• 2010

We study affine translation surfaces in $\mathbb{R}^3$ and get a complete classification of such surfaces with constant Gauss-Kronecker curvature.

• Bulletin of the Korean Mathematical Society
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• v.54 no.6
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• pp.2119-2139
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• 2017

Here, certain Ricci flow for Finsler n-manifolds is considered and deformation of Cartan hh-curvature, as well as Ricci tensor and scalar curvature, are derived for spaces of scalar flag curvature. As an application, it is shown that on a family of Finsler manifolds of constant flag curvature, the scalar curvature satisfies the so-called heat-type equation. Hence on a compact Finsler manifold of constant flag curvature of initial non-negative scalar curvature, the scalar curvature remains non-negative by Ricci flow and blows up in a short time.

• The Pure and Applied Mathematics
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• v.22 no.2
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• pp.113-125
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• 2015

We study half lightlike submanifolds M of an indefinite trans-Sasakian manifold of quasi-constant curvature subject to the condition that the 1-form θ and the vector field ζ, defined by (1.1), are identical with the 1-form θ and the vector field ζ of the indefinite trans-Sasakian structure { J, θ, ζ } of .

• Communications of the Korean Mathematical Society
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• v.31 no.2
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• pp.365-377
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• 2016

In this paper, we study half lightlike submanifolds M of an indefinite Kaehler manifold $\bar{M}$ of quasi-constant curvature such that the characteristic vector field ${\zeta}$ of $\bar{M}$ is tangent to M. First, we provide a new result for such a half lightlike submanifold. Next, we investigate a statical half lightlike submanifold M of $\bar{M}$ subject such that (1) the screen distribution S(TM) is totally umbilical or (2) M is screen conformal.

• East Asian mathematical journal
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• v.32 no.1
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• pp.1-11
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• 2016

We study transversal half lightlike submanifolds of an indefinite Kaehler manifold of a quasi-constant curvature. First, we provide a new result for such a transversal half lightlike submanifold. Next, we investigate a statical half lightlike submanifold M such that (1) the screen distribution S(TM) is totally umbilical, or (2) M is screen homothetic.

• Journal of the Korean Mathematical Society
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• v.44 no.4
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• pp.799-807
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• 2007

In this paper we study non-simply connected Riemannian manifolds of constant positive curvature which have an orbit of codimension one under the action of a connected closed Lie subgroup of isometries. When the action is reducible we characterize the orbits explicitly. We also prove that in some cases the manifold is homogeneous.

• Journal of the Korean Mathematical Society
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• v.52 no.3
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• pp.523-535
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• 2015

We study surfaces in Euclidean space which are obtained as the sum of two curves or that are graphs of the product of two functions. We consider the problem of finding all these surfaces with constant Gauss curvature. We extend the results to non-degenerate surfaces in Lorentz-Minkowski space.

• Communications of the Korean Mathematical Society
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• v.12 no.1
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• pp.101-108
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• 1997

We let (M,g) be a noncompact complete Riemannina manifold of dimension $n \geq 3$ with finite volume and positive scalar curvature. We show the existence of a conformal metric with constant positive scalar curvature on (M,g) by gluing solutions of Yamabe equation on each compact subsets $K_i$ with $\cup K_i = M$ .

• Bulletin of the Korean Mathematical Society
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• v.42 no.1
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• pp.39-44
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• 2005

Let M be a compact hypersurface in hyperbolic space and let A be the area of M and V be the volume of the compact domain bounded by M. In this paper, we find a lower bound for $\frac{A}{V}$ in two cases, M has constant scalar curvature and M has constant mean curvature.

• Bulletin of the Korean Mathematical Society
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• v.50 no.5
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• pp.1567-1586
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• 2013

In this paper, we study the Einstein multiply warped products with a semi-symmetric non-metric connection and the multiply warped products with a semi-symmetric non-metric connection with constant scalar curvature, we apply our results to generalized Robertson-Walker spacetimes with a semi-symmetric non-metric connection and generalized Kasner spacetimes with a semi-symmetric non-metric connection and find some new examples of Einstein affine manifolds and affine manifolds with constant scalar curvature. We also consider the multiply warped products with an affine connection with a zero torsion.