• Honam Mathematical Journal
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• v.36 no.4
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• pp.723-730
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• 2014

In the present paper, we introduce a type of Riemannian manifolds (namely, $W_4$-birecurrent manifold) and study the several properties of such a manifold on which some geometric conditions are imposed.

• Honam Mathematical Journal
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• v.30 no.4
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• pp.693-701
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• 2008

In this paper, when N is a compact Riemannian manifold of class (A), we consider the nonexistence of some warping functions on space-times M = $[a,{\infty}){\times}_fN$ with prescribed scalar curvatures.

• East Asian mathematical journal
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• v.18 no.2
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• pp.235-243
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• 2002

In this paper, we get conditions for the natural projections of some product manifolds with varying metrics of two Riemannian manifolds to be harmonic, and necessary and sufficient conditions for some product manifolds with the harmonic natural projections of two Einstein manifolds to be Einstein manifolds.

• Journal of the Korean Mathematical Society
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• v.33 no.1
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• pp.169-181
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• 1996

Let $x : M^n \longrightarrow E^m$ be an isometric immersion of an n-dimensional connected Riemannian manifold into the m-dimensional Euclidean space. Then the metric tensor on $M^n$ is naturally induced from that of $E^m$.

• Bulletin of the Korean Mathematical Society
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• v.54 no.3
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• pp.967-973
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• 2017

We prove that a homogeneous square Einstein Finsler metric is either Riemannian or flat.

• Journal of the Korean Mathematical Society
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• v.43 no.6
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• pp.1289-1300
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• 2006

It is well known that the twistor, section of twistor space, classify the orthogonal almost complex structure on even dimensional Riemannian manifold (X, g). We will show that existence of a harmonic and anti-holomorphic twistor is equivalent to having a symplectic structure on (X, g).

• Bulletin of the Korean Mathematical Society
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• v.28 no.2
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• pp.231-241
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• 1991

Recently, many mathematicians([NT], [Ka], [TV], [CW], etc.) studied foliated structures on a smooth manifold with the viewpoint of transversal differential geometry. In this paper, we shall discuss certain hermitian foliations F on a riemannian manifold with a bundle-like metric, that is, their transversal bundles to F have hermitian structures.

• The Pure and Applied Mathematics
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• v.3 no.2
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• pp.173-179
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• 1996

M be an ($n\geq3$)-dimensional compact connected and oriented Riemannian manifold isometrically immersed on an (n ＋ 2)-dimensional sphere $S^{n＋2}$(c). If all sectional curvatures of M are not less than a positive constant c, show that M is a real homology sphere.

• Honam Mathematical Journal
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• v.22 no.1
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• pp.107-111
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• 2000

We study Einstein warped product spaces. As a result, we prove the following: if M is an Einstein warped product space with base a compact 2-dimensional surface, then M is simply a Riemannian product space.

• Bulletin of the Korean Mathematical Society
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• v.37 no.1
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• pp.85-90
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• 2000

On Riemannian manifolds of dimension 4 the Einstein condition is equivalent to the Thorpe condition. In this paper, we construct a few metrics which we Einstein but not Thorpe, and vice versa in dimensions larger than 4.