簡易檢索 / 詳目顯示
| 研究生： |
李宗源 Lee, Tsung-Yuan |
|---|---|
| 論文名稱： |
海森堡群H_1上的馬尤厄-卡當形式及其應用 The Maurer-Cartan form on the Heisenberg group H_1 and its application |
| 指導教授： |
邱鴻麟
Chiu, Hung-Lin |
| 口試委員: |
陳瑞堂
Chen, Jui-Tang 賴馨華 Lai, Sin-Hua |
| 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： | 2024 |
| 畢業學年度： | 112 |
| 語文別： | 英文 |
| 論文頁數： | 24 |
| 中文關鍵詞： | 微分幾何 、海森堡群 、馬尤厄-卡當形式 |
| 外文關鍵詞： | Maurer-Cartan form, Darboux derivative |
| 相關次數： | 點閱：23 下載：0 |
| 分享至: |
| 查詢本校圖書館目錄 查詢臺灣博碩士論文知識加值系統 勘誤回報 |
本文中我們將介紹馬尤厄-卡當形式及卡當定理。接下來將其應用在海森堡群$H_1$，尤其著重在Pansu-Sphere上並計算高斯曲率。
In this thesis, we introduce the Maurer-Cartan form and the Cartan's theorem. We apply them on the Heisenberg group H_1, especially on the the Pansu-Sphere to calculate the Gaussian curvature.
1.Hung-Lin Chiu; Yen-Chang Huang; Sin-Hua Lai, An application of the moving frame method to integral geometry in the Heisenberg group, Symmetry Integrability Geom. Methods Appl., 13 (2017), (SCI)
2.Chiu, Hung-Lin; Liu, Hsiao-Fan, A characterization of constant p−mean curvature surfaces in the Heisenberg group H_1, Advances in Mathematics, 405(2022), (SCI)
3.Thomas A. Ivey; J. M. Landsberg, Cartan for Beginners: Differential Geometry Via Moving Frames and Exterior Differential Systems, Graduate Studies in Mathematics, Volume 61, American Mathematical Society, 2003.
4.Chern S.S.; Chen W.H.; Lam K.S., Lectures on Differential Geometry, Series on University Mathematics, Vol.1, World Scientific Publishing Company, 1999.
5.Manfredo P. Do Carmo, Differential Geometry of Curves and Surfaces: Revised and Updated Second Edition, Dover Publications, 2017.