• Honam Mathematical Journal
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• v.42 no.1
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• pp.151-160
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• 2020

In this paper, we obtain some necessary and sufficient conditions such that a semi-slant submanifold in a locally product Riemannian manifold reduces to a warped product semi-slant submanifold and also give an example supported this characterization.

• Honam Mathematical Journal
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• v.44 no.1
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• pp.1-16
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• 2022

In this paper, we define and study warped product skew semi-invariant submanifolds of a locally golden Riemannian manifold. We investigate a necessary and sufficient condition for a skew semi-invariant submanifold of a locally golden Riemannian manifold to be a locally warped product. An equality between warping function and the squared normed second fundamental form of such submanifolds is established. We also construct an example of warped product skew semi-invariant submanifolds.

• Honam Mathematical Journal
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• v.36 no.3
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• pp.597-603
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• 2014

In this paper, we prove the existence of warping functions on Riemannian warped product manifolds with fiber manifold of class (B) having some prescribed scalar curvatures.

• Korean Journal of Mathematics
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• v.23 no.4
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• pp.733-740
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• 2015

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

• Journal of Integrative Natural Science
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• v.5 no.1
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• pp.42-45
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• 2012

In this paper, when N is a compact Riemannian manifold, we discuss the nonexistence of conformal deformations on Riemannian warped product manifold $M=({\alpha},\;{\infty}){\times}_fN$ with prescribed scalar curvature functions.

• Journal of the Chungcheong Mathematical Society
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• v.24 no.2
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• pp.171-185
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• 2011

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

• Kyungpook Mathematical Journal
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• v.60 no.1
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• pp.197-210
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• 2020

In this paper, we prove that there are no non-trivial 𝒫ℛ-semi-slant warped product submanifolds with proper slant coefficients in para-Kähler manifolds ${\bar{M}}$. We also present a numerical example that illustrates the existence of a 𝒫ℛ-warped product submanifold in ${\bar{M}}$.

• 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).

• Journal of the Chungcheong Mathematical Society
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• v.26 no.3
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• pp.525-532
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• 2013

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

• The Pure and Applied Mathematics
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• v.10 no.2
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• pp.119-126
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• 2003

In this paper, when N is a compact Riemannian manifold, we considered the positive time solution to equation $\Box_gu(t,x)-c_nu(t,x)+c_nu(t,x)^{(n+3)/(n-1)}$ on M ＝$(-{\infty},+{\infty})\;{\times}_f\;N$, where $c_n$ ＝(n－1)/4n and $\Box_{g}$ is the d'Alembertian for a Lorentzian warped manifold.