在二維黎曼流形上的四頂點定理
The Four-vertex Theorem in Riemannian 2-manifolds
在二維黎曼流形上的四頂點定理
The Four-vertex Theorem in Riemannian 2-manifolds
Date
2006
Authors
黃志強
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Abstract
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.
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.
Description
Keywords
頂點,
曲率,
外接圓,
四頂點定理,
vertex,
curvature,
circumscribed circle,
four-vertex theorem