• 대한수학회논문집
• /
• 제39권1호
• /
• pp.201-210
• /
• 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
• /
• 제51권4호
• /
• pp.411-417
• /
• 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
• /
• 제59권2호
• /
• pp.277-291
• /
• 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.

• 대한수학회논문집
• /
• 제30권2호
• /
• pp.109-121
• /
• 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.

• 호남수학학술지
• /
• 제1권1호
• /
• pp.11-14
• /
• 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.

• 대한수학회논문집
• /
• 제33권1호
• /
• pp.305-315
• /
• 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.

• 호남수학학술지
• /
• 제40권4호
• /
• pp.681-689
• /
• 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.

• 대한수학회논문집
• /
• 제37권3호
• /
• pp.893-904
• /
• 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.

• 한국콘텐츠학회:학술대회논문집
• /
• 한국콘텐츠학회 2003년도 춘계종합학술대회논문집
• /
• pp.470-473
• /
• 2003

우주를 표현하는 시공간은 중력, 척력등 여러 가지 요인으로 심하게 굴곡되어진 공간일것이라는 이론이 관찰로 입증되었다. 그러므로 시공간의 연구는 다증 비틀림 공간의 연구를 있게 했고 앞으로도 더 많은 연구가 있게 될것으로 기대된다. 본 연구는 다중 비틀림 공간에서의 지표정리의 적용으로 Roberson-Walker 시공간에 대한 연구이다. 지표정리는 시공간의 특이성과 밀접한 관계를 가지므로 Roberson-Walker 시공간에서의 특이성조건을 조사하였다.

• 대한수학회논문집
• /
• 제34권2호
• /
• pp.633-635
• /
• 2019

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