论文标题
在正曲率中的奇异riemannian叶子的核心减少
Core reduction for singular Riemannian foliations in positive curvature
论文作者
论文摘要
我们表明，对于配备奇异的riemannian叶叶的光滑歧管，如果叶的度量指标具有正截面曲率，并且存在一个前截面，那是适当的子曼叶术，可以保留叶面的所有横向几何信息，则叶片空间具有边界。特别是，我们看到弯曲的歧管的极性叶面具有具有非空边界的叶片空间。
We show that for a smooth manifold equipped with a singular Riemannian foliation, if the foliated metric has positive sectional curvature, and there exists a pre-section, that is a proper submanifold retaining all the transverse geometric information of the foliation, then the leaf space has boundary. In particular, we see that polar foliations of positively curved manifolds have leaf spaces with nonempty boundary.
