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完整後設資料紀錄
DC 欄位 | 值 | 語言 |
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dc.contributor.advisor | 王金龍 | |
dc.contributor.author | Shih-Kai Chiu | en |
dc.contributor.author | 邱詩凱 | zh_TW |
dc.date.accessioned | 2021-05-15T17:50:48Z | - |
dc.date.available | 2014-08-25 | |
dc.date.available | 2021-05-15T17:50:48Z | - |
dc.date.copyright | 2014-08-25 | |
dc.date.issued | 2014 | |
dc.date.submitted | 2014-08-19 | |
dc.identifier.citation | [EH89] Klaus Ecker and Gerhard Huisken. Mean curvature evolution of entire graphs. Annals of Mathematics, pages 453–471, 1989.
[Hit97] Nigel Hitchin. The moduli space of special lagrangian submanifolds. arXiv preprint dg-ga/9711002, 1997. [HL82] Reese Harvey and H Blaine Lawson. Calibrated geometries. Acta Mathematica, 148(1):47–157, 1982. [Joy03] Dominic Joyce. Riemannian holonomy groups and calibrated geometry. Springer, 2003. [Mar02] Stephen P Marshall. Deformations of special Lagrangian submanifolds. PhD thesis, University of Oxford, 2002. [McL96] Robert C McLean. Deformations of calibrated submanifolds. In Commun. Analy. Geom. Citeseer, 1996. [PW91] Giorgio Patrizio and Pit-Mann Wong. Stein manifolds with compact symmetric center. Mathematische Annalen, 289(1):355–382, 1991. [Sei97] Paul Seidel. Floer homology and the symplectic isotopy problem. PhD thesis, University of Oxford, 1997. [Smo96] Knut Smoczyk. A canonical way to deform a lagrangian submanifold. arXiv preprint dg-ga/9605005, 1996. [Ste93] Matthew B Stenzel. Ricci-flat metrics on the complexification of a compact rank one symmetric space. Manuscripta Mathematica, 80(1):151–163, 1993. | |
dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/4991 | - |
dc.description.abstract | 在 Seidel 的博士論文 [Sei97] 中,他與他的指導教授 Donaldson 證明,若一緊緻凱勒流形 (compact Kahler manifold) 擁有一個尋常退化 (ordinary degeneration),則此凱勒流形內存在拉格朗日球面 (Lagrangian sphere)。這個結果引發以下的延伸問題:如果此凱勒流形為一卡拉比 -丘流形 (Calabi-Yau manifold),我們是否能夠在其中找出一個特殊拉格朗日球面 (special Lagrangian sphere)?透過文獻回顧,我們將探討特殊拉格朗日子流形 (special Lagrangian submanifolds) 的基本知識,以及球面的切叢 (the cotangent bundle of sphere) 上的瑞奇平坦度量 (Ricci-flat metrics)。在論文的最後,我們透過均曲率流 (mean curvature flow) 來探討一維的情形。 | zh_TW |
dc.description.abstract | In his PhD thesis[Sei97], Paul Seidel and his advisor Simon K. Donaldson gave two proofs showing that a vanishing cycle in a Kahler manifold admitting an ordinary degener- ation can be chosen to be Lagrangian. This gives rise to the question whether the vanishing cycle is special Lagrangian if the manifold is Calabi-Yau. We investigate this problem by reviewing the geometric aspect of special Lagrangian manifolds and the Ricci-flat met- rics on the noncompact local model, namely the cotangent bundle of sphere. Finally, we approach this problem in dimension one through mean curvature flow. | en |
dc.description.provenance | Made available in DSpace on 2021-05-15T17:50:48Z (GMT). No. of bitstreams: 1 ntu-103-R01221031-1.pdf: 449213 bytes, checksum: 63093e4e479abf5dfd2b3c99563ed335 (MD5) Previous issue date: 2014 | en |
dc.description.tableofcontents | Contents
口試委員會審定書 i 謝辭 ii 中文摘要 iii Abstract iv 1 Introduction 1 2 Special Lagrangian Geometry 2 2.1 Definitions and Basic Results........................ 2 2.2 McLean’s Theorem............................. 3 2.3 Geometric Structures on the Local Moduli Spaces . . . . . . . . . . . . . 9 3 Ricci-flat metrics on T^∗ S^n 15 3.1 Existence of the Metric........................... 15 3.2 Completeness of the Stenzel Metric .................... 19 3.3 Special Lagrangian Structures ....................... 21 4 Existence of Lagrangian Spheres 23 4.1 Seidel’s Proof................................ 24 4.2 Donaldson’s Proof ............................. 27 5 Discussion on the Main Problem 29 5.1 Formulation of the Main Problem ..................... 29 5.2 Results in n=1............................... 30 | |
dc.language.iso | en | |
dc.title | 特殊拉格朗日球面存在性問題之探討 | zh_TW |
dc.title | On the Existence Problem of Special Lagrangian Spheres | en |
dc.type | Thesis | |
dc.date.schoolyear | 102-2 | |
dc.description.degree | 碩士 | |
dc.contributor.oralexamcommittee | 張樹城,蔡忠潤 | |
dc.subject.keyword | 特殊拉格朗日子流形,瑞奇平坦度量, | zh_TW |
dc.subject.keyword | special Lagrangian submanifolds,Ricci-flat metrics, | en |
dc.relation.page | 36 | |
dc.rights.note | 同意授權(全球公開) | |
dc.date.accepted | 2014-08-19 | |
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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