径向曲率的Alexandrov-Toponogov比较定理
The Alexandrov-Toponogov comparison theorem for radial curvature
摘要：
本文在点流形（M，o）以旋转旋转曲面为参照的径向曲率条件下，讨论了Alexandrov-Toponogov比较定理.对于其中一个顶点是基点o的三角形，建立比较定理有两个障碍。一个是参考旋转曲面中比较三角形的另一个顶点的割点。另一类是M中基点o的割点。我们找到了一个条件，在此条件下，对于M中顶点为o的任意测地三角形，omp定理成立。
英文摘要：
We discuss the Alexandrov-Toponogov comparison theorem under the conditions of radial curvature of a pointed manifold (M,o) with reference surface of revolution. There are two obstructions to make the comparison theorem for a triangle one of whose vertices is a base point o. One is the cut points of another vertex of a comparison triangle in the reference surface of revolution. The other is the cut points of the base point o in M. We find a condition under which the omparison theorem is valid for any geodesic triangle with a vertex at o in M.
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