论文标题
洛伦兹歧管上的空间叶子
Spacelike Foliations on Lorentz manifolds
论文作者
论文摘要
在这项工作中，我们研究了Lorentz歧管上的Hypersurfaces的间距类叶的几何特性。我们研究叶子稳定，完全大地或完全脐带的条件。我们认为$ \叠加{m}^{n+1} $配备了序列式的封闭形式矢量字段$ξ$。如果叶面具有恒定的平均曲率，我们表明叶子是稳定的。当叶子是紧凑的间距性高空时，我们表明，在某些条件下，它是完全脐带的。对于通过完全非伴随性超曲面的叶子，我们使用无穷大的最大原理来得出结论，叶面完全是测量的。
In this work, we study the geometric properties of spacelike foliations by hypersurfaces on a Lorentz manifold. We investigate conditions for the leaves being stable, totally geodesic or totally umbilical. We consider that $\overline{M}^{n+1}$ is equipped with a timelike closed conformal vector field $ξ$. If the foliation has constant mean curvature, we show that the leaves are stable. When the leaves are compact spacelike hypersurfaces we show that, under certain conditions, its are totally umbilic hypersurfaces. In the case of foliations by complete noncompact hypersurfaces, we using a Maximum Principle at infinity to conclude that the foliation is totally geodesic.
