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| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 王藹農(Ai-Nung Wang) | |
| dc.contributor.author | Chao-Wei Liang | en |
| dc.contributor.author | 梁釗瑋 | zh_TW |
| dc.date.accessioned | 2021-06-16T09:17:31Z | - |
| dc.date.available | 2017-07-20 | |
| dc.date.copyright | 2017-07-20 | |
| dc.date.issued | 2017 | |
| dc.date.submitted | 2017-07-11 | |
| dc.identifier.citation | References
[1] Dominic D.Joyce Compact 8-manifolds with holonomy Spin(7). (1996) [2] Dominic D.Joyce Compact Manifolds with Special Holonomy. (2000) [3] Dominic D.Joyce Riemannian Holonomy Groups and Calibrated Geometry. (2007) [4] Dominic D.Joyce Compact riemannian 7-manifolds with holonomy G2 I. (1996) [5] Dominic D.Joyce Compact riemannian 7-manifolds with holonomy G2 II. (1996) [6] Dominic D.Joyce Compact Riemannian Manifolds with Exceptional Holonomy. (1999) [7] Christine Taylor Compact Manifolds with Holonomy Spin(7). (1996) [8] Simon Salamon Riemannian geometry and holonomy groups. (1989) [9] Robert L.Bryant Metric with exceptional holonomy. (1987) [10] Anthony W. Knapp Lie Groups Beyond an Introduction, Second Edition. (2002) [11] Raoul Bott and Loring W. Tu Differential Forms in Algebraic Topology. (1982) [12] Claude Chevalley and Samuel Eilenberg Cohomology Theory of Lie Groups and Lie Algebras. (1948) [13] John W. Milnor and James D. Stasheff Characteristic classes. (1974) [14] John M. Lee Introduction to smooth manifolds. (2002) [15] Jurgen Jost Riemannian Geometry and Geometric Analysis. (2008) [16] Phillip Griffiths and Joseph Harris Principles of Algebraic Geometry. (1994) | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/59191 | - |
| dc.description.abstract | 在Berger 對非對稱流形Holonomy group 的分類中，Spin(7) 為一個特例，八維流形可能會有Spin(7) 的Holonomy group，而第一個緊緻且有Spin(7) Holonomy group 的流形是由Dominic Joyce 所構造，在這篇文章中會討論Joyce 構造流形的過程。 | zh_TW |
| dc.description.abstract | In Berger’s classification of holonomy groups of non-symmetric manifolds, Spin(7) is a special case. The first compact manifold with holonomy Spin(7) is constructed by Dominic Joyce in 1996. In this article, we will discuss Joyce’s construction of such manifolds. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-16T09:17:31Z (GMT). No. of bitstreams: 1 ntu-106-R02221024-1.pdf: 373614 bytes, checksum: 8d412438c6e5273dba3f4642daa28b2c (MD5) Previous issue date: 2017 | en |
| dc.description.tableofcontents | 口試委員審定書i
誌謝ii 中文摘要iii Abstract iv 1 Introduction 1 1.1 Holonomy groups . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Spin(7) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.3 Forms and Spin(7)-structures . . . . . . . . . . . . . . . . . . . . 4 1.4 Eguchi-Hanson space and Kummer construction . . . . . . . . . . 5 1.5 Sobolev space, Sobolev norm . . . . . . . . . . . . . . . . . . . . 7 2 Crucial Theorems and Steps to construct manifolds with holonomy Spin(7) 7 2.1 Crucial Theorems . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.2 Steps to construct manifolds with holonomy Spin(7) . . . . . . . 9 3 Construction of 8-manifolds 9 3.1 Resolving singularities of orbifolds . . . . . . . . . . . . . . . . . 9 3.2 8-manifolds with holonomy Spin(7) . . . . . . . . . . . . . . . . . 12 References 16 | |
| dc.language.iso | en | |
| dc.subject | 流形 | zh_TW |
| dc.subject | 和樂群 | zh_TW |
| dc.subject | 李群 | zh_TW |
| dc.subject | 旋量群 | zh_TW |
| dc.subject | 微分形式 | zh_TW |
| dc.subject | Spin | en |
| dc.subject | Lie group | en |
| dc.subject | differential form | en |
| dc.subject | holonomy | en |
| dc.subject | manifold | en |
| dc.title | Holonomy為Spin(7)的緊緻八維流形 | zh_TW |
| dc.title | Compact 8-manifolds with holonomy Spin(7) | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 105-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 蔡宜洵,崔茂培 | |
| dc.subject.keyword | 流形,和樂群,旋量群,微分形式,李群, | zh_TW |
| dc.subject.keyword | manifold,holonomy,Spin,differential form,Lie group, | en |
| dc.relation.page | 16 | |
| dc.identifier.doi | 10.6342/NTU201701435 | |
| dc.rights.note | 有償授權 | |
| dc.date.accepted | 2017-07-12 | |
| 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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