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題名 | A Characterization for Surfaces of Constant Curvature by Eigenfunctions=常曲率曲面之固有函數 |
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作者姓名(中文) | 許義容; | 書刊名 | Proceedings of the National Science Council : Part A, Physical Science and Engineering |
卷期 | 22:2 1998.03[民87.03] |
頁次 | 頁171-177 |
分類號 | 319.9 |
關鍵詞 | 常曲率曲面; 固有函數; Eigenforms; Eigenfunctions; Surfaces of constant curvature; |
語文 | 英文(English) |
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。此結果推廣作者一非負曲率的結果 ,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 | aThis paper concentrates on the problem of characterizing surfaces of constant curvature by means of eigenfunctions of the Laplace-Beltrami operator. The main result shows that if a surface has two eigenfunctions, ii and v, having the same nonzero eigenvalue such that the square of u+iv, is also an eigenfunction corresponding to some complex eigenvalue, then the surface is of constant curvature. This result gives a characterization of surfaces of constant curvature K with K>O, K=0 and K<O, respectively. Finally, we apply these results to an analogus problem on closed eicen 1-forms. |
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