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| ???org.dspace.app.webui.jsptag.ItemTag.dcfield??? | Value | Language |
|---|---|---|
| dc.contributor.advisor | 李瑩英(Yng-Ing Lee) | |
| dc.contributor.author | Shu-Ting Huang | en |
| dc.contributor.author | 黃書庭 | zh_TW |
| dc.date.accessioned | 2021-06-17T03:49:00Z | - |
| dc.date.available | 2018-02-26 | |
| dc.date.copyright | 2018-02-26 | |
| dc.date.issued | 2018 | |
| dc.date.submitted | 2018-01-22 | |
| dc.identifier.citation | [1] W. Ambrose and I. M. Singer. A theorem on holonomy. Transactions of the American Mathematical Society, 75(3):428–443, 1953.
[2] Marcel Berger. Sur les groupes d’holonomie homogenes des varietes a connexion affines et des varietes riemanniennes. Bulletin de la Societe Mathematique de France, 83:279–330, 1955. [3] Robert Bryant. Some remarks on G2-structures. [4] Robert Bryant. Metrics with exceptional holonomy. Annals of mathematics, 126(3): 525–576, 1987. [5] Reesse Harvey and H. Blaine Lawson. Calibrated geometries. Acta Mathematica, 148(1):47–157, 1982. [6] Dominic D. Joyce. Compact Manifolds with Special Holonomy. 2000. [7] Dominic D. Joyce. Riemannian Holonomy Groups and Calibrated Geometry. 2007. [8] Robert C. Mclean. Deformations of calibrated submanifold. Communications in Analysis and Geometry, 6(4):705–747, 1998. | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/70200 | - |
| dc.description.abstract | 本論文為將介紹帶有特殊和樂群G2與Spin(7)的流形，利用校準以及八元數對此主題進行深入探討，最後討論結合子流形、餘結合子流形、Cayley子流形的形變向量場。 | zh_TW |
| dc.description.abstract | This thesis is a brief survey of manifolds with exceptional holonomy groups G2 and Spin(7). These two holonomy groups come from Berger’s classification [2]. In chapter 2, I introduce some basic properties of the group G2 and
Spin(7), most of these results and proofs are from [4], [6], [7]. Chapter 3 is an introduction to the notion of calibration and octonions, and use octonion to discover more insights of the G2 and Spin(7) geometry. The examples of calibrated submanifolds we are going to study are associative, coassociative and Cayley submanifolds. Chapter 4 gives a discussion about the deformation vector fields of these calibrated submanifolds, which is from Mclean’s paper [8]. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-17T03:49:00Z (GMT). No. of bitstreams: 1 ntu-107-R01221009-1.pdf: 969451 bytes, checksum: 95a951b703e5f3551eb025bbffb4272c (MD5) Previous issue date: 2018 | en |
| dc.description.tableofcontents | 口試委員審定定書 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .i
致謝 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii 中文摘要 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .iii Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .iv Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1 Classification of Holonomy Groups . . . . . . . . . . . . . . . . . . . . . 1 2 Manifolds with Exceptional Holonomy Groups . . . . . . . . . . . . . . . . . 4 2.1 The G2 Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.2 The Spin(7) Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 3 Calibrations in Manifolds with Exceptional Holonomy and Octonions . . . . . .19 3.1 Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .19 3.2 Octonion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 4 Calibrated Submanifolds in Manifolds with Exceptional Holonomy . . . . . . . 25 4.1 Coassociative Submanifold . . . . . . . . . . . . . . . . . . . . . . . . .25 4.2 Associative Submanifold . . . . . . . . . . . . . . . . . . . . . . . . . .27 4.3 Cayley Submanifold . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 A Clifford Algebras, Spinors and Dirac Operators . . . . . . . . . . . . . . . 33 A.1 Clifford Algebras . . . . . . . . . . . . . . . . . . . . . . . . . . . . .33 A.2 Dirac Operators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .34 A.3 Spin structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 B Homotopy Exact Sequence of a Fiber Bundle . . . . . . . . . . . . . . . . . .37 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 | |
| dc.language.iso | en | |
| dc.subject | 校準 | zh_TW |
| dc.subject | 八元數 | zh_TW |
| dc.subject | Cayley 子流形 | zh_TW |
| dc.subject | Spin(7) 流形 | zh_TW |
| dc.subject | G2 流形 | zh_TW |
| dc.subject | 餘結合子流形 | zh_TW |
| dc.subject | 結合子流形 | zh_TW |
| dc.subject | Cayley submanifold | en |
| dc.subject | Spin(7) manifold | en |
| dc.subject | calibration | en |
| dc.subject | octonion | en |
| dc.subject | associative submanifold | en |
| dc.subject | coassociative submanifold | en |
| dc.subject | G2 manifold | en |
| dc.title | 特殊和樂群流形及其校準子流形 | zh_TW |
| dc.title | Manifolds with Exceptional Holonomy Groups and Their Calibrated Submanifolds | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 106-1 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 崔茂培(Mao-Pei Tsui),蔡忠潤(Chung-Jun Tsai),鄭日新(Jih-Hsin Cheng) | |
| dc.subject.keyword | G2 流形,Spin(7) 流形,校準,八元數,結合子流形,餘結合子流形,Cayley 子流形, | zh_TW |
| dc.subject.keyword | G2 manifold,Spin(7) manifold,calibration,octonion,associative submanifold,coassociative submanifold,Cayley submanifold, | en |
| dc.relation.page | 38 | |
| dc.identifier.doi | 10.6342/NTU201800134 | |
| dc.rights.note | 有償授權 | |
| dc.date.accepted | 2018-01-23 | |
| dc.contributor.author-college | 理學院 | zh_TW |
| dc.contributor.author-dept | 數學研究所 | zh_TW |
| Appears in Collections: | 數學系 | |
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| File | Size | Format | |
|---|---|---|---|
| ntu-107-1.pdf Restricted Access | 946.73 kB | Adobe PDF |
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