论文标题
赋予产品结构的4个manifolds中的无效曲面
Null hypersurfaces in 4-manifolds endowed with a product structure
论文作者
论文摘要
在4个manifold中，riemannian爱因斯坦度量标准的组成几乎是等距且平行的几乎是偏ad子复合结构的，它定义了一个中性度量，该度量公平且标量平坦。在本文中，我们研究了相对于这种中性度量的空洞，尤其是我们研究了它们相对于爱因斯坦度量标准的几何特性。首先，我们表明所有完全测量的零超曲面都是标量平坦的，它们的存在意味着环境歧管中的爱因斯坦度量必须是ricci-flat。然后，我们发现存在具有相同非平凡的主曲率的无效性超表面的必要条件，最后，我们在环境标态曲率上给出了必要的条件，因为存在恒定平均曲率的无（非微小）高度曲面。
In a 4-manifold, the composition of a Riemannian Einstein metric with an almost paracomplex structure that is isometric and parallel, defines a neutral metric that is conformally flat and scalar flat. In this paper, we study hypersurfaces that are null with respect to this neutral metric and in particular we study their geometric properties with respect to the Einstein metric. Firstly, we show that all totally geodesic null hypersurfaces are scalar flat and their existence implies that the Einstein metric in the ambient manifold must be Ricci-flat. Then, we find a necessary condition for the existence of null hypersurface with equal non-trivial principal curvatures and finally, we give a necessary condition on the ambient scalar curvature, for the existence of null (non-minimal) hypersurfaces that are of constant mean curvature.
