论文标题
在球形罗伯逊 - 步行器时空研究间距submanifolds的新方法
A new approach to the study of spacelike submanifolds in a spherical Robertson-Walker spacetime: characterization of the stationary spacelike submanifolds as an application
论文作者
论文摘要
每个$（n+1）$ - 尺寸球形的Robertson-Walker（RW）spacetime $ i \ times_f \ times_f \ Mathbb {s}^n $ in $（n+2）$（n+2）$ - dimentz-mink-minkski spacizki spacike-spaceTime $ \ mathbb { \ Mathbb {s}^n $作为$ \ mathbb {l}^{n+2} $的旋转lorentzian hypersurface。在对这种Lorentzian Hypersurfaces进行了详细研究之后，可以将这种RW时空的任何$ k $二维的超级式submanifold视为$ \ Mathbb {l}^{n+2} $的$ \ mathbb {l}^{l}然后，我们利用这种情况来研究RW时空的$ K $维固定（即零平均曲率矢量场）的间隔submanifolds。特别是，我们证明了洛伦兹（Lorentzian）版本的古典高桥定理（Takahashi Theorem）的广泛延伸，从而描述了$ i \ times_f \ times_f \ mathbb {s}^n $的固定固定空间submanifolds，而当它们将它们视为$ \ mathbb的spacelike submanifolds时，
A natural one codimension isometric embedding of each $(n+1)$-dimensional spherical Robertson-Walker (RW) spacetime $I\times_f \mathbb{S}^n$ in $(n+2)$-dimensional Lorentz-Minkowski spacetime $\mathbb{L}^{n+2}$ permits to contemplate $I\times_f \mathbb{S}^n$ as a rotation Lorentzian hypersurface of $\mathbb{L}^{n+2}$. After a detailed study of such Lorentzian hypersurfaces, any $k$-dimensional spacelike submanifold of such an RW spacetime can be contemplated as a spacelike submanifold of $\mathbb{L}^{n+2}$. Then, we use that situation to study $k$-dimensional stationary (i.e., of zero mean curvature vector field) spacelike submanifolds of the RW spacetime. In particular, we prove a wide extension of the Lorentzian version of the classical Takahashi theorem, giving a characterization of stationary spacelike submanifolds of $I\times_f \mathbb{S}^n$ when contemplating them as spacelike submanifolds of $\mathbb{L}^{n+2}$.
