论文标题
仿射歧管上的线性叶子
Linear foliations on affine manifolds
论文作者
论文摘要
在本文中，我们研究了具有线性叶子的仿射歧管。这些是线性载体不变的矢量子空间定义的叶子。我们表明，如果$ {\ cal f}的叶子仅由$ n $ dimenslional contection，$ n $二维的紧凑，完整和定向的仿射歧管，并带有一个编成$ 1 $ 1 $线性叶片$ {\ cal f} $的$ n $ dimensomlion-dimensmolic，如果$ {\ cal f} $的叶子是同粒子的。令$（m，\ nabla_m）$为$ 3 $二维紧凑型仿射歧管，并带有一个编成$ 1 $的线性叶子。我们证明，$（m，\ nabla_m）$具有有限的封面，如果其开发地图是iNjementive，并且具有凸面图像，则与圆圈的总空间同构。
In this paper, we study affine manifolds endowed with linear foliations. These are foliations defined by vector subspaces invariant by the linear holonomy. We show that an $n$-dimensional compact, complete, and oriented affine manifold endowed with a codimension $1$ linear foliation ${\cal F}$ is homeomophic to the $n$-dimensional torus if the leaves of ${\cal F}$ are simply connected. Let $(M,\nabla_M)$ be a $3$-dimensional compact affine manifold endowed with a codimension $1$ linear foliation. We prove that $(M,\nabla_M)$ has a finite cover which is homeomorphic to the total space of a bundle over the circle if its developing map is injective, and has a convex image.
