林俊吉黃志強2019-09-052006-7-272019-09-052006http://etds.lib.ntnu.edu.tw/cgi-bin/gs32/gsweb.cgi?o=dstdcdr&s=id=%22GN0693400025%22.&%22.id.&http://rportal.lib.ntnu.edu.tw:80/handle/20.500.12235/101718我們研究從1909年開始的頂點定理之結果。更進一步，我們著重於在二維黎曼流形上的曲線，並且推廣奧瑟曼的證明。在這篇論文，某些二維黎曼流形上特殊曲線的四頂點定理被得到。We survey the results on the four-vertex theorems, beginning from 1909. Moreover, we focus on curves in Riemannian 2-manifolds and generalize the Osserman’s proof [6]. Some four-vertex theorems for special curves in Riemannian 2-manifolds are derived in this thesis.頂點曲率外接圓四頂點定理vertexcurvaturecircumscribed circlefour-vertex theorem