一族新的具有简单割迹的纬向波纹双旋球
A new family of latitudinally corrugated two-spheres of revolution with simple cut locus
摘要：
虽然我们知道在欧几里得空间中人们非常熟悉的旋转曲面，如椭球面、双叶双曲面、抛物面和环面的割迹结构，但还没有确定许多种旋转曲面的割迹结构。除了环面，已知的割迹结构非常简单，即，一个点或一个弧。本文引入了一类新的具有简单割迹结构的2-旋转球族{M_n}_n。这个家庭也是新的意义上说，在每个子午线上的点的数量，其中假设一个局部极小值或最大值的高斯曲率函数的子午线上去无穷大，因为n去无穷大。
英文摘要：
There are not so many kinds of surface of revolution whose cut locus structure have been determined, although the cut locus structures of very familiar surfaces of revolution (in Euclidean space) such as ellipsoids, 2-sheeted hyperboloids, paraboloids, and tori are now known. Except for tori, the known cut locus structures are very simple, i.e., a single point or an arc. In this article, a new family {M_n}_n of 2-spheres of revolution with simple cut locus structure is introduced. This family is also new in the sense that the number of points on each meridian which assume a local minimum or maximum of the Gaussian curvature function on the meridian goes to infinity as n goes to infinity.
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。
