• 대한수학회보
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• 제50권5호
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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.

• Korean Journal of Mathematics
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• 제23권3호
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• pp.479-489
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• 2015

We study the GMGHS spacetime to analyze anisotropic cosmology model which represents homogeneous but anisotropically expanding(contracting)cosmology. In this paper we investigate the solution of GMGHS spacetime in form of doubly warped products possessing warping functions and find the Ricci curvature associated with three phases in the evolution of the universe.

• 대한수학회지
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• 제42권5호
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• pp.1101-1110
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• 2005

Recently, Chen studied warped products which are CR-submanifolds in Kaehler manifolds and established general sharp inequalities for CR-warped products in Kaehler manifolds. In the present paper, we obtain sharp estimates for the squared norm of the second fundamental form (an extrinsic invariant) in terms of the warping function for contact CR-warped products isometrically immersed in Kenmotsu space forms. The equality case is considered. Some applications are derived.

• 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.

• 호남수학학술지
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• 제46권1호
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• pp.47-59
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• 2024

The purpose of the Nash embedding theorem was to take extrinsic help for studying the intrinsic Riemannian geometry. To realize this aim in actual practice there is a need for optimal relationships between the known intrinsic invariants and the main extrinsic invariants for Riemannian submanifolds. This paper aims to provide an optimal relationship for CR-warped product submanifolds of locally conformal Kähler manifolds.

• 호남수학학술지
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• 제20권1호
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• pp.153-159
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• 1998

• 대한수학회보
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• 제41권4호
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• pp.691-697
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• 2004

In this paper we find index form of the multiply warped product manifolds to investigate the physical properties from space-time.

• 대한수학회지
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• 제55권3호
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• pp.553-574
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• 2018

In this paper, we study harmonic maps and biharmonic maps on the principal G-bundle in Kobayashi and Nomizu and also the warped product $P=M{\times}_fF$ for a $C^{\infty}$(M) function f on M studied by Bishop and O'Neill, and Ejiri.

• 호남수학학술지
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• 제28권2호
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• pp.233-240
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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 constant scalar curvature.

• 호남수학학술지
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• 제42권1호
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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.