论文标题
Ricci孤子和曲率遗传在Robinson-Trautman的空间上
Ricci solitons and curvature inheritance on Robinson-Trautman spacetimes
论文作者
论文摘要
本文的目的是研究RICCI孤子的存在以及曲率遗传的性质以及在Robinson-Trautman（简短，RT）时空上的插条。结果表明，在某些条件下，RT Spacetime承认了几乎Ricci Soliton，几乎是$η$ -Ricci Soliton，几乎梯度$η$ -Ricci Soliton。作为曲率继承的概括\ cite {duggal1992}和曲率colleation \ cite \ cite {kld1969}，在本文中，我们介绍了\ textIt {gentrizatized curvator sastaritance}的概念，并检查了rt spaceTime spaceTime允许这样的记录。结果表明，RT时空还意识到了广义曲率（RICCI，Weyl共形，偶联，Conharmonic，Weyl joxpiveive）的遗传。最后，获得了几种条件，在这些条件下，RT时段具有曲率（分别是Ricci，ricci，conharmonic，Weyl joffimitive）的继承和曲率（分别ricci，ricci，weyl songormal，weyl conformal，circular，congircular，conharmonic，conharmonic，weyl joftive），我们还介绍了一般性的谎言概念，并介绍了一般性的遗传概念。
The purpose of the article is to investigate the existence of Ricci solitons and the nature of curvature inheritance as well as collineations on the Robinson-Trautman (briefly, RT) spacetime. It is shown that under certain conditions RT spacetime admits almost Ricci soliton, almost $η$-Ricci soliton, almost gradient $η$-Ricci soliton. As a generalization of curvature inheritance \cite{Duggal1992} and curvature collineation \cite{KLD1969}, in this paper, we introduce the notion of \textit{generalized curvature inheritance} and examine if RT spacetime admits such a notion. It is shown that RT spacetime also realizes the generalized curvature (resp. Ricci, Weyl conformal, concircular, conharmonic, Weyl projective) inheritance. Finally, several conditions are obtained, under which RT spacetime possesses curvature (resp. Ricci, conharmonic, Weyl projective) inheritance as well as curvature (resp. Ricci, Weyl conformal, concircular, conharmonic, Weyl projective) collineation, and we have also introduced the concept of generalized Lie inheritance and showed that RT spacetime realizes such a notion.
