• 대한수학회지
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• 제60권1호
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• pp.143-165
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• 2023

For each connected and simply connected three-dimensional non-unimodular Lie group, we classify the left invariant Lorentzian metrics up to automorphism, and study the extent to which curvature can be altered by a change of metric. Thereby we obtain the Ricci operator, the scalar curvature, and the sectional curvatures as functions of left invariant Lorentzian metrics on each of these groups. Our study is a continuation and extension of the previous studies done in [3] for Riemannian metrics and in [1] for Lorentzian metrics on unimodular Lie groups.

• 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.

• 대한수학회지
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• 제59권4호
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• pp.651-684
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• 2022

Let G be an arbitrary, connected, simply connected and unimodular Lie group of dimension 3. On the space 𝔐(G) of left-invariant Lorentzian metrics on G, there exists a natural action of the group Aut(G) of automorphisms of G, so it yields an equivalence relation ≃ on 𝔐(G), in the following way: h₁ ≃ h₂ ⇔ h₂ = 𝜙^*(h₁) for some 𝜙 ∈ Aut(G). In this paper a procedure to compute the orbit space Aut(G)/𝔐(G) (so called moduli space of 𝔐(G)) is given.

• 대한수학회논문집
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• 제38권1호
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• pp.195-203
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• 2023

Special examples of harmonic manifolds that are not symmetric, proving that the conjecture posed by Lichnerowicz fails in the non-compact case have been intensively studied. We completely classify homogeneous structures on Damek-Ricci spaces equipped with the left invariant metric.

• 대한수학회보
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• 제56권1호
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• pp.229-243
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• 2019

We use the so-called pseudoinversion of degenerate metrics technique on foliated compact null hypersurface, $M^{n+1}$, in Lorentzian manifold ${\overline{M}}^{n+2}$, to derive an integral formula involving the r-th order mean curvatures of its foliations, ${\mathcal{F}}^n$. We apply our formula to minimal foliations, showing that, under certain geometric conditions, they are isomorphic to n-dimensional spheres. We also use the formula to deduce expressions for total mean curvatures of such foliations.

• 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.

• 대한수학회논문집
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• 제29권2호
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• pp.319-329
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• 2014

In this paper we study the properties of conformally recurrent pseudo Riemannian manifolds admitting a proper conformal vector field with respect to the scalar field ${\sigma}$, focusing particularly on the 4-dimensional Lorentzian case. Some general properties already proven by one of the present authors for pseudo conformally symmetric manifolds endowed with a conformal vector field are proven also in the case, and some new others are stated. Moreover interesting results are pointed out; for example, it is proven that the Ricci tensor under certain conditions is Weyl compatible: this notion was recently introduced and investigated by one of the present authors. Further we study conformally recurrent 4-dimensional Lorentzian manifolds (space-times) admitting a conformal vector field: it is proven that the covector ${\sigma}_j$ is null and unique up to scaling; moreover it is shown that the same vector is an eigenvector of the Ricci tensor. Finally, it is stated that such space-time is of Petrov type N with respect to ${\sigma}_j$.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제5권2호
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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.