平面子空间本质上是CAT（0）
Planar subspaces are intrinsically CAT(0)
摘要：
设$M_k$是完备的单连通的常曲率黎曼2-流形$k \le 0$ .设$E$是$M_k$的一个闭单连通子空间，满足$E$中的每两点由$E$中的可求长路连通.证明了在诱导路径度量下，$E$是完备CAT（$k$）空间.我们还表明，自然的角度概念来自内在和外在的度量一致的所有简单的测地线三角形。
英文摘要：
Let $M_k$ be the complete, simply connected, Riemannian 2-manifold of constant curvature $k \le 0$. Let $E$ be a closed, simply connected subspace of $M_k$ with the property that every two points in $E$ is connected by a rectifiable path in $E$. We show that under the induced path metric, $E$ is a complete CAT($k$) space. We also show that the natural notions of angle coming from the intrinsic and extrinsic metrics coincide for all simple geodesic triangles.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
