• Bulletin of the Korean Mathematical Society
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• v.41 no.4
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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.

• Honam Mathematical Journal
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• v.27 no.2
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• pp.273-285
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• 2005

In this paper, when N is a compact Riemannian manifold, we discuss the method of using warped products to construct Lorentzian metrics on $M=[a,\;b){\times}_f\;N$ with specific scalar curvatures.

• Bulletin of the Korean Mathematical Society
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• v.37 no.2
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• pp.317-336
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• 2000

In this paper, when N is a compact Riemannian manifold, we discuss the method of using warped products to construct timelike or null future (or past) complete Lorentzian metrics on $M=(-{\infty},{\;}\infty){\;}{\times}f^N$ with specific scalar curvatures.

• The Pure and Applied Mathematics
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• v.5 no.2
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• pp.115-122
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• 1998

In this paper, when N is a compact Riemannian manifold, we discuss the method of using warped products to construct timelike or null future(or past) complete Lorentzian metrics on $M{\;}={\;}[a,{\;}{\infty}){\times}_f{\;}N$ with specific scalar curvatures.

• The Pure and Applied Mathematics
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• v.6 no.2
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• pp.95-101
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• 1999

In this paper, when N is a compact Riemannian manifold, we discuss the method of using warped products to construct timelike or null future complete Lorentzian metrics on $M{\;}={\;}[\alpha,\infty){\times}_f{\;}N$ with specific scalar curvatures.

• Proceedings of the Korea Contents Association Conference
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• 2003.11a
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• pp.367-372
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• 2003

In the framework of Lorentzian warped products, we study the Friedmann - Robertson - Walker cosmological model to investigate non-smooth curvatures associated with multiple discontinuities involved in the evolution of the universe. In particular we analyze non-smooth features of the spatially flat Friedmann-Robertson-Walker universe by introducing double discontinuities occurred at the radiation- matter and matter-lambda phase transitions in astrophysical phenomenology.