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A surface M in a Euclidean 3space is said to be of finite type if each of its coordinate functions is a finite sum of eigenfunctions of the Laplacian operator on M with respect to the induced metric (cf. [1,2]). Minimal surface are the simplest examples of surfaces of finite type, in fact, minimal surfaces are of ltype. The spheres, minimal surfaces and circular cylinders are the only known exampls of surfaces of finite type in E3 and it seems to be the only finite type surfaces in E3 (cf. [5]). The first author conjectured in [2] that spheres are the only compact finite type surfaces in E3. Since then, it was prived step by sted and separately that finite type tubes, finite type ruled surfaces, finite type quadrics and finite type cones are surfaces of the only known examples (cf. [2,6,7,10].) Our next natural target for this classification problem is the class of surfaces of revolution. However, this case seems to be much difficult than the other cases mentioned above. 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On classification of some surfaces of revolution of finite type
http://hdl.handle.net/2241/7268
06947ce471ab439d829e0d6782fd130c
Name / File  License  Actions  

20.pdf (743.2 kB)


item type  Departmental Bulletin Paper(1)  

公開日  20070308  
タイトル  
タイトル  On classification of some surfaces of revolution of finite type  
言語  
言語  eng  
資源タイプ  
タイプ  departmental bulletin paper  
著者 
Chen, Bangyen
× Chen, Bangyen× Ishikawa, Susumu 

抄録  
内容記述  In this article, we study the following problem of [5]: Classify all finite type surfaces in a Euclidean 3space E3. A surface M in a Euclidean 3space is said to be of finite type if each of its coordinate functions is a finite sum of eigenfunctions of the Laplacian operator on M with respect to the induced metric (cf. [1,2]). Minimal surface are the simplest examples of surfaces of finite type, in fact, minimal surfaces are of ltype. The spheres, minimal surfaces and circular cylinders are the only known exampls of surfaces of finite type in E3 and it seems to be the only finite type surfaces in E3 (cf. [5]). The first author conjectured in [2] that spheres are the only compact finite type surfaces in E3. Since then, it was prived step by sted and separately that finite type tubes, finite type ruled surfaces, finite type quadrics and finite type cones are surfaces of the only known examples (cf. [2,6,7,10].) Our next natural target for this classification problem is the class of surfaces of revolution. However, this case seems to be much difficult than the other cases mentioned above. We therefore investigate this classification problem for this class and obtain classification theorems for surfaces of revolution which are either of rational or of polynomial kinds (cf. §1 for the definitions). As consequence, further supports for the conjecture cited above are obtained.  
書誌情報 
Tsukuba journal of mathematics 巻 17, 号 1, p. 287298, 発行日 199306 

ISSN  
収録物識別子  03874982  
書誌レコードID  
収録物識別子  AA00874643  
著者版フラグ  
値  author  
出版者  
出版者  Institute of Mathematics, University of Tsukuba  
URI  
識別子  http://hdl.handle.net/2241/7268 