• Communications of the Korean Mathematical Society
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• v.39 no.1
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• pp.201-210
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• 2024

This paper is concerned with the study of spacetimes satisfying div 𝓜 = 0, where "div" denotes the divergence and 𝓜 is the m-projective curvature tensor. We establish that a perfect fluid spacetime with div 𝓜 = 0 is a generalized Robertson-Walker spacetime and vorticity free; whereas a four-dimensional perfect fluid spacetime becomes a Robertson-Walker spacetime. Moreover, we establish that a Ricci recurrent spacetime with div 𝓜 = 0 represents a generalized Robertson-Walker spacetime.

• Kyungpook Mathematical Journal
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• v.51 no.4
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• pp.411-417
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• 2011

In the present paper, we are concerned with subordination problems related to ${\lambda}$-Robertson function. The radii of ${\lambda}$-spirallikeness and starlikeness of ${\lambda}$-Robert function are also determined.

• Kyungpook Mathematical Journal
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• v.59 no.2
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• pp.277-291
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• 2019

Using the concept of bounded boundary rotation, we investigate various properties of two new generalized classes of spirallike and Robertson functions of complex order with bounded boundary rotations.

• Communications of the Korean Mathematical Society
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• v.30 no.2
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• pp.109-121
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• 2015

In this paper, we investigate horizontal lightlike hypersurfaces of Robertson-Walker spacetimes. Some results involving the unique existence of the screen distribution and the symmetry of the induced Ricci curvature tensor of horizontal lightlike hypersurfaces are presented. We also obtain some properties concerning the symmetry and the parallelism of the second fundamental forms of such lightlike hypersurfaces.

• Honam Mathematical Journal
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• v.1 no.1
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• pp.11-14
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• 1979

S^{**}를 S의 subclass로서$f(z)=z+a_zz^2+{\cdots}\;{\cdots}\;{\cdots}\;{\cdots}$가 $Re\{zf^'(z)[f(z)-f(-z)]^{-1}\}$>0, ${\left|z\right|}$<1을 만족하는 함수족(函數族)이라 하자. M.S. Robertson은 1961년에 subordination의 원리를 이용하여 $f(z)=z+a_zz^2+{\cdots}\;{\cdots}\;{\cdots}$가 S^{**}에 속하기 위한 충분조건을 구하였다. 본(本) 논문(論文)은 Robertson의 조건에 약간의 수정을 가해서 f(Z)가 S^{**}에 속하기 위한 필요 충분 조건을 만들고, 그것을 증명하였다.

• Communications of the Korean Mathematical Society
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• v.33 no.1
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• pp.305-315
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• 2018

This note provides a study of lightlike hypersurfaces of a generalized Robertson-Walker(GRW) space-time with a certain screen distribution, which are integrable and have good properties. Focus is to investigate geometric features from the relation of the second fundamental forms between lightlike hypersurfaces and leaves of the integrable screen distribution. Also, we shall apply those results on lightlike hypersurfaces of a GRW space-time to lightlike hypersurfaces of a Robertson-Walker(RW) space-time.

• Honam Mathematical Journal
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• v.40 no.4
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• pp.681-689
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• 2018

In this paper, we defined new subclasses of Spirallike and Robertson functions by using concept of q-derivative operator. We investigate convolution properties and coefficient estimates for both classes q-Spirallike and q-Robertson functions denoted by ${\mathcal{S}}^{\lambda}_q[A,\;B]$ and ${\mathcal{C}}^{\lambda}_q[A,\;B]$, respectively.

• Communications of the Korean Mathematical Society
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• v.37 no.3
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• pp.893-904
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• 2022

In this note, we apply a maximum principle related to volume growth of a complete noncompact Riemannian manifold, which was recently obtained by Alías, Caminha and do Nascimento in [4], to establish new uniqueness and nonexistence results concerning maximal spacelike hypersurfaces immersed in a generalized Robertson-Walker (GRW) spacetime obeying the timelike convergence condition. A study of entire solutions for the maximal hypersurface equation in GRW spacetimes is also made and, in particular, a new Calabi-Bernstein type result is presented.

• Proceedings of the Korea Contents Association Conference
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• 2003.05a
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• pp.470-473
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• 2003

We have the index form of the multiply warped products manifold. From this result we will investigate the physical properties on the Robertson-Walker spacetime. The singularly thorem are usually interpreted as an indication that black hole exist and that there has been a big bang. This paper include necessary condition for the Robertson-Walker spacetime with singularly.

• Communications of the Korean Mathematical Society
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• v.34 no.2
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• pp.633-635
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• 2019

In this note we show that Lorentzian Concircular Structure manifolds $(LCS)_n$ coincide with Generalized Robertson-Walker space-times.