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http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/68070完整後設資料紀錄
| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 蔡忠潤(Chung-Jun Tsai) | |
| dc.contributor.author | Chung-Ming Pan | en |
| dc.contributor.author | 潘仲銘 | zh_TW |
| dc.date.accessioned | 2021-06-17T02:12:07Z | - |
| dc.date.available | 2018-02-26 | |
| dc.date.copyright | 2018-02-26 | |
| dc.date.issued | 2017 | |
| dc.date.submitted | 2017-12-29 | |
| dc.identifier.citation | [1] Nicholas Buchdahl. On compact Kähler surfaces. 49(1):287-302, 1999.
[2] Huai-Dong Cao. Deformation of Kähler matrics to Kähler-Einstein metrics on compact Kähler manifolds. Inventiones mathematicae, 81(2):359-372, 1985. [3] Paul Gauduchon. Le théorème de l'excentricité nulle. Comptes Rendus Hebdomadaires des S{’e}ances de l'Académie des Sciences. Séries A et B, 285:387-390, 1977. [4] Paul Gauduchon and Liviu Ornea. Locally conformally Kähler metrics on Hopf surfaces. 48(4):1107-1127, 1998. [5] Matt Gill. Convergence of the parabolic complex Monge-Ampère equation on compact Hermitian manifolds. Communications in analysis and geometry, 19(2):277-304, 2011. [6] Kunihiko Kodaira. On the structure of complex analytic surfaces, I. American Journal of Mathematics, 86:751-798, 1964. [7] Andrei Teleman. The pseudo-effective cone of a non-Kählerian surface and applications. Mathematische Annalen, 335(4):965-989, 2006. [8] Valentino Tosatti and Ben Weinkove. On the evolution of a Hermitian metric by its Chern-Ricci form. Journal of Differential Geometry, 99(1):125-163, 2015. [9] Shing-Tung Yau. On the Ricci curvature of a compact Kähler manifold and the complex Monge-Ampère equation, I. Communications on pure and applied mathematics, 31(3):339-411, 1978. | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/68070 | - |
| dc.description.abstract | 本文主要在研究陳里奇流在具有埃米爾特點積的複流型上，並介紹了一些Tosatti與Weinkove所證明的重要的結果。此外，我們也研討了陳里奇流在一些非凱勒曲面上的行為。第一部分中我們主要介紹了一些陳里奇流的現代結果與我們的結果。第二部分為讀者方便起見，收錄了一些基本的術語合常用的記號。第三至第七部分則介紹了一些Tosatti與Weinkove的定理證明。最後，我們嘗試了在廣義的霍普夫曲面上，使用用特殊的戈迪雄點積調查陳里奇流。 | zh_TW |
| dc.description.abstract | In this master thesis, we study the Chern-Ricci flow on the complex Hermitian manifolds and introduce the results proved by Tosatti and Weinkove.
Moreover, we investigate the Chern-Ricci flow on some non-Kähler surfaces. In the first section, we introduce some modern results of the Chern-Ricci flow and our result. In the second part, we include some well-known notation and conventions for reader’s convenience. From the third part to the seventh part, we introduce the proofs of some modern theorems proved by Tosatti and Weinkove. Finally, we investigate the Chern-Ricci flow starting with a special Gauduchon metric on the general Hopf surfaces. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-17T02:12:07Z (GMT). No. of bitstreams: 1 ntu-106-R04221008-1.pdf: 910274 bytes, checksum: 20ec91d9cd07995c747bd11849e17bd8 (MD5) Previous issue date: 2017 | en |
| dc.description.tableofcontents | 1 Introduction 2
2 Notation and Conventions 6 3 Evolution of r{hat{g}} g 8 4 Parabolic Monge-Ampere Flow and Maximal Existence Time 14 5 Negative First Chern Class and Kähler-Einstein Metric 22 6 Finite Maximal Existence Time 26 7 Classification of Surfaces with respect to the Chern-Ricci flow 31 8 Hopf Surfaces 36 Reference 42 | |
| dc.language.iso | en | |
| dc.subject | 陳里奇曲率張量 | zh_TW |
| dc.subject | 安立奎-小平分類定理 | zh_TW |
| dc.subject | 霍普夫曲面 | zh_TW |
| dc.subject | 複流型 | zh_TW |
| dc.subject | 凱勒-愛因斯坦點積 | zh_TW |
| dc.subject | Complex manifolds | en |
| dc.subject | Chern-Ricci curvature | en |
| dc.subject | Kahler-Einstein metric | en |
| dc.subject | Enriques-Kodaira classification | en |
| dc.subject | Hopf surfaces | en |
| dc.title | 複流型上的陳里奇流 | zh_TW |
| dc.title | Chern-Ricci flow on Complex Manifolds | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 106-1 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 崔茂培(Mao-Pei Tsui),馬梓銘(Ziming Nikolas Ma) | |
| dc.subject.keyword | 複流型,陳里奇曲率張量,凱勒-愛因斯坦點積,安立奎-小平分類定理,霍普夫曲面, | zh_TW |
| dc.subject.keyword | Complex manifolds,Chern-Ricci curvature,Kahler-Einstein metric,Enriques-Kodaira classification,Hopf surfaces, | en |
| dc.relation.page | 42 | |
| dc.identifier.doi | 10.6342/NTU201701568 | |
| dc.rights.note | 有償授權 | |
| dc.date.accepted | 2017-12-29 | |
| dc.contributor.author-college | 理學院 | zh_TW |
| dc.contributor.author-dept | 數學研究所 | zh_TW |
| 顯示於系所單位： | 數學系 | |
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