- 作者: 許義容
- 作者服務機構: 國立交通大學應用數學系
- 中文摘要: 本文旨在找出常曲率曲面之拉普拉斯算子之固有函數的特徵。主要結果為:若一曲面上存在兩個對應相同非零固有值之固有函數u與v;其複數函數u+iv之平方亦為一對應某複數固有值之固有函數,則該曲面必為常曲率。此結果推廣作者-非負曲率的結果,得以適用於負曲率,並能順利應用到固有式之特徵問題上“
- 英文摘要: This paper concentrates on the problem of characterizing surfaces of constant curvature by meansof eigenfunctions of the Laplace-Beltrami operator. The main result shows that if a surface has twoeigenfunctions,u and v, having the same nonzero eigenvalue such that the square of a+iv is also aneigenfunction corresponding to some complex eigenvalue, then the surface is of constant curvature.Thisresult gives a characterization of surfaces of constant curvature K with K>0, K=0 and K<0, respectively.Finally, we apply these results to an analogus problem on closed eigen 1-forms.
- 中文關鍵字: eigenforms; eigenfunctions; surfaces of constant curvature
- 英文關鍵字: --