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| 研究生： |
張哲禮 Che-Li Chang |
|---|---|
| 論文名稱： |
調合映射在幾何上的性質 Geometry of harmonic maps |
| 指導教授： |
張樹城
Shu-Cheng Chang |
| 口試委員: | |
| 學位類別： |
碩士 Master |
| 系所名稱： |
理學院 - 數學系 Department of Mathematics |
| 論文出版年： | 2008 |
| 畢業學年度： | 96 |
| 語文別： | 英文 |
| 論文頁數： | 21 |
| 中文關鍵詞： | 調合映射 |
| 外文關鍵詞： | harmonic maps |
| 相關次數： | 點閱：2 下載：0 |
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This main idea is to report the application of harmonic maps on geometries[Xin] . First of all , we start out to define essential abstracts of differential geometry and a lot of properties we need . And then we derive the first variational formula , the Bochner’s formula ,and the second variational formula. Those conclude the material of differential geometry and geometry analysis . At last , we have some conclusions of the monotonicity inequality .
[Xin] Y. L. Xin , Geometry of harmonic maps , Bikha ̈user Boston 1996.
[E-S] J. Eells and J. H. Sampson , Harmonic mappings of Riemannian manifolds ,
Amer. J. Math. 86 (1964) , 106-160.
[Se] H. C. J. Sealey , Harmonic maps of small energy , Bull. London Math .Soc.V13 (5) (1981) , 405-408.
[S-Y] R. Schoen and S. T. Yau , Harmonic maps and the topology of stable hypersurfaces and manifolds with nonnegative Ricci curvature , Comment.. Math. Helv . 39 (1976) , 333-341.
[Le] P. F. Leung , On the stability of harmonic maps , Springer-Verlag Lecture Notes Math. 949 (1982) , 122-129.
[B-E] P. Baird and J. Eells , A conservation law for harmonic maps ,Springer-Verlag Lecture Notes Math. 894 (1981) , 1-15.
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