Affine functions on Alexandrov surfaces
Affine functions on Alexandrov surfaces
复制标题
Alexandrov 曲面上的仿射函数
DOI：
10.18910/9165
复制
发表时间：
1999
影响因子：
0.4
通讯作者：
Yukihiro Mashiko
中科院分区：
文献类型：
--
作者：
Yukihiro Mashiko
一个亚历山德罗夫曲面X是一个2-Hausdorff维的，连通的，局部紧的和完全长度的空间，其曲率在亚历山德罗夫意义下是有界的，没有边界点。对于一个点x G X，x是从x发出的所有测地线方向的集合，配备了角度量Z。设λ x是λ x的度量完备化。我们称之为x方向空间。这对应于黎曼几何中的单位切球。对于任意x G X的方向空间λ x是圆周的圆> X上的R称为凸的当且仅当对于任意测地线7：[α，B] -> X和任意λ G [0，1]：
An Alexandrov surface X is by definition a 2-Hausdorff dimensional, connected, locally compact and complete length space of curvature bounded from below in the sense of Alexandrov which has no boundary points. For a point x G X, Σ x is the set of all directions of geodesies emanating from x equipped with the angular metric Z. Let Σx be the metric completion of Σ x . We call it the space of directions at x. This corresponds to the unit tangent sphere in Riemannian geometry. The space of directions Σ x for each x G X is either a circle of circumference > R on X is called convex iff the following inequality holds for an arbitrary geodesic 7 : [α, b] —> X and arbitrary λ G [0,1]: