论文标题
维度4中的曲率均匀流形
Curvature homogeneous manifolds in dimension 4
论文作者
论文摘要
我们将完整的曲率均匀度量分类为简单地连接的四个维歧管，这些歧管在同时性一个动作下是不变的。我们表明，它们要么是具有其同时性一个动作之一的对称空间的等距，要么是Tsukada在CP^2中Veronese表面的正常束上的完整示例。在途中，我们（在任何维度）表明，通过模棱两可的差异性，描述度量标准的函数可以部分地对角度化，这一事实也可能对其他问题有用
We classify complete curvature homogeneous metrics on simply connected four dimensional manifolds which are invariant under a cohomogeneity one action. We show that they are either isometric to a symmetric space with one of its cohomogeneity one actions, or to a complete example by Tsukada on the normal bundle of the Veronese surface in CP^2. Along the way we show (in any dimension) that via an equivariant diffeomorphism the functions describing the metric can be partially diagonalized, a fact that may be useful for other problems as well
