• 호남수학학술지
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• 제44권1호
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• pp.62-77
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• 2022

This study presents an 𝛼-Sasakian structure on the product manifold M₁ × 𝛽(I), where M₁ is a Kähler manifold with an exact 1-form, and 𝛽(I) is an open curve. It then defines a new type warped product metric to study the warped product of almost Hermitian manifolds with almost contact metric manifolds, contact metric manifolds, and K-contact manifolds.

• 호남수학학술지
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• 제29권4호
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• pp.641-647
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• 2007

In this paper, we consider the problem of achieving constant scalar curvature on warped product manifolds according to fiber manifolds with constant scalar curvature.

• 대한수학회논문집
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• 제35권1호
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• pp.261-268
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• 2020

In this paper, we study gradient Yamabe solitons in the warped product manifolds and classify the warped product manifolds with gradient Yamabe solitons. Moreover we investigate the admitness of gradient Yamabe solitons and geometric structures for some model spaces.

• 대한수학회지
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• 제46권5호
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• pp.979-995
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• 2009

As warped product manifolds provide an excellent setting to model space time near black holes or bodies with large gravitational field, the study of these manifolds assumes significance in general. B. Y. Chen [4] initiated the study of CR-warped product submanifolds in a Kaehler manifold. He obtained a characterization for a CR-submanifold to be locally a CR-warped product and an estimate for the squared norm of the second fundamental form of CR-warped products in a complex space form (cf [6]). In the present paper, we have obtained a necessary and sufficient conditions in terms of the canonical structures P and F on a CR-submanifold of a nearly Kaehler manifold under which the submanifold reduces to a locally CR-warped product submanifold. Moreover, an estimate for the second fundamental form of the submanifold in a generalized complex space is obtained and thus extend the results of Chen to a more general setting.

• 호남수학학술지
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• 제28권3호
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• pp.399-407
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• 2006

In this paper, we consider the problem of achieving a prescribed scalar curvature on warped product manifolds according to fiber manifolds with zero scalar curvature.

• 충청수학회지
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• 제28권4호
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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).

• 충청수학회지
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• 제24권2호
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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.

• 대한수학회논문집
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• 제38권2호
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• pp.547-560
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• 2023

For a pseudo-slant submanifold of a Kenmotsu manifold, we have worked out conditions in terms its canonical structure tensors, T and F, and its shape operator so that it reduces to a warped product submanifold.

• 호남수학학술지
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• 제40권3호
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• pp.447-456
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• 2018

In this paper, we consider nonconstant warping functions on Einstein Lorentzian warped product manifolds $M=B{\times}_{f^2}F$ with an 1-dimensional base B which has a negative definite metric. As the results, we discuss that on M the resulting Einstein Lorentzian warped product metric is a future (or past) geodesically complete one outside a compact set.

• 충청수학회지
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• 제35권3호
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• pp.235-242
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• 2022

In this paper, we consider the existence of nonconstant warping functions on a warped product manifold M = B × _f² F, where B is a q(> 2)-dimensional base manifold with a nonconstant scalar curvature S_B(x) and F is a 3- dimensional fiber Einstein manifold and discuss that the resulting warped product manifold is an Einstein manifold, using the existence of the solution of some partial differential equation.