• 대한수학회보
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• 제60권6호
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• pp.1641-1650
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• 2023

It is our goal in this study to present the structure of isotropic mean Berwald Finsler warped product metrics. We bring out the rich class of warped product Finsler metrics behaviour under this condition. We show that every Finsler warped product metric of dimension n ≥ 2 is of isotropic mean Berwald curvature if and only if it is a weakly Berwald metric. Also, we prove that every locally dually flat Finsler warped product metric is weakly Berwaldian. Finally, we prove that every Finsler warped product metric is of isotropic Berwald curvature if and only if it is a Berwald metric.

• 호남수학학술지
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• 제39권2호
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• pp.187-197
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• 2017

In this paper, we prove the existence of warping functions on Lorentzian warped product manifolds and the completeness of the resulting metrics with some prescribed scalar curvatures.

• 호남수학학술지
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• 제37권1호
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• pp.127-134
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• 2015

In this paper, we prove the existence of warping functions on Lorentzian warped product manifolds and the completeness of the resulting metrics with some prescribed scalar curvatures.

• 대한수학회보
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• 제59권6호
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• pp.1359-1370
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• 2022

In this paper, we study the Finsler warped product metric which is dually flat or projectively flat. The local structures of these metrics are completely determined. Some examples are presented.

• 대한수학회보
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• 제41권1호
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• pp.117-123
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• 2004

It has been conjectured that, on a compact orient able manifold M, a critical point of the total scalar curvature functional restricted the space of unit volume metrics of constant scalar curvature is Einstein. In this paper we show that if a manifold is a 3-dimensional warped product, then (M, g) cannot be a critical point unless it is isometric to the standard sphere.

• Korean Journal of Mathematics
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• 제23권4호
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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).

• 호남수학학술지
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• 제27권2호
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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.

• 대한수학회보
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• 제37권2호
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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.

• 한국수학교육학회지시리즈A:수학교육
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• 제33권1호
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• pp.123-128
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• 1994

• Journal of applied mathematics & informatics
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• 제29권1_2호
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• pp.497-504
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• 2011

In 1973, B. Y. Chen and K. Yano introduced the special conformally flat space for the generalization of a subprojective space. The typical example is a canal hypersurface of a Euclidean space. In this paper, we study the conditions for the base space B to be special conformally flat in the conharmonically flat warped product space $B^n{\times}_fR^1$. Moreover, we study the special conformally flat warped product space $B^n{\times}_fF^p$ and characterize the geometric structure of $B^n{\times}_fF^p$.