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http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/50528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 | Chao-Ming Lin | en |
| dc.contributor.author | 林朝明 | zh_TW |
| dc.date.accessioned | 2021-06-15T12:44:42Z | - |
| dc.date.available | 2016-08-02 | |
| dc.date.copyright | 2016-08-02 | |
| dc.date.issued | 2016 | |
| dc.date.submitted | 2016-07-26 | |
| dc.identifier.citation | [1] Berger, M. Sur les groupes d’holonomie homog`enes de vari ́et ́es a` connexion affine et des vari ́et ́es riemanniennes. Bulletin de la Soci ́et ́e Math ́ematique de France 83 (1955), 279–330.
[2] Berlin, T. F., Berlin, I. K., Paris, A. M., and Berlin, U. S. On Nearly Parallel G2-Structures. 0–29. [3] Brown, R. B., and Gray, A. Vector cross products. Commentarii Mathematici Helvetici 42, 1 (1967), 222–236. [4] Bryant, R., and Salamon, S. On construction of some complete metrics with exceptional holonomy. Duke Math. J. 58, 3 (1989), 829. [5] Bryant, R., and Xu, F. Laplacian Flow for Closed G2-Structures: Short Time Behavior. 20. [6] Bryant, R. L. Metrics with exceptional holonomy. Annals of mathematics 126, 3 (1987), 525–576. [7] Bryant, R. L. Some remarks on G2-structures. 211–224. [8] Fine, J. A gauge theoretic approach to the anti-self-dual Einstein equations. arXiv : 1111 . 5005v2 [ math . DG ] 29 Nov 2011 (2011). [9] Grigorian, S. Short-time behaviour of a modified Laplacian coflow of G2-structures. Advances in Mathematics 248 (2013), 378–415. [10] Hamilton, R. S. The inverse function theorem of Nash and Moser. Bulletin of the American Mathematical Society 7, 1 (1982), 65–223. [11] Hitchin, N. The geometry of three-forms in six and seven dimensions. 2000. arXiv preprint math.dg/0010054 (2008), 1–38. [12] Joyce, D. D. Compact Riemannian 7-manifolds with holonomy G2. I. Journal of Differential Geometry 43, 2 (1996), 329–375. [13] Joyce, D. D. Compact Riemannian 7-manifolds with holonomy G2. II. Journal of Differential Geometry 43, 2 (1996), 329–375. [14] Joyce; Dominic D. Compact Manifolds with Special Holonomy.pdf, 2000. [15] Karigiannis, S. Deformations of G2 and Spin(7) Structures on Manifolds. 1–17. [16] Karigiannis, S. Flows of G2-structures. 12. [17] Lawson, H. B., Lawson, H. B., Michelsohn, M.-L., and Michelsohn, M.-L. Spin geometry. 1989. [18] Lotay, J. D., and Wei, Y. Laplacian flow for closed G2 structures: Shi-type estimates, uniqueness and compactness. 1–52. [19] Lotay, J. D., and Wei, Y. Stability of torsion-free G2 structures along the Laplacian flow. 1–24. [20] Salamon, D. Riemannian geometry and holonomy groups. Acta Applicandae Mathematicae 20, 3 (1990), 309–311. [21] Weber, P. Introduction to definite connection. | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/50528 | - |
| dc.description.abstract | 本文主要在研究 G2 流形上的幾何性質，以及與其相關的主題。本文主要分為三個部分，第一部分給出了有關 G2 流形基本性質的定義與重新證明，舉例來說如果一個七維流形是一個 G2 流形的話，那它存在一個愛因斯坦點積，而且是里奇平坦流形。第二部分整理了目前主要在 G2 流形上的體積函數，例如 Hitchin 的體積函數，並分析了其在極值點附近是否有好的性質。第三部分給出了一種在某些主叢上造出愛因斯坦點積的方法，準確來說，我們在上面造出了一個 co-closed G2 結構並滿足了幾乎平行的性質，所以推得在主叢上有一個愛因斯坦點積是由 co-closed G2 結構給出。 | zh_TW |
| dc.description.abstract | In this master thesis, we study the G2 geometry and some relevant topics. There are three main sections in this master thesis, in the first part, we state the definitions and reprove some general facts of G2 geometry, for example, if a 7-dimensional manifold is a G2 manifold, then there exists an Einstein metric on it, moreover, the metric is Ricci flat. In the second part, we summarize some volume functional on G2 manifold in date, for example, the Hitchin's volume functional, and we analyze the stability at the critical points. In the third section, we construct an Einstein metric on certain principal bundle, technically, we give a construction of co-closed G2-structure satisfies the nearly parallel condition, hence the principal bundle contains an Einstein metric which is induced by the co-closed G2-structure. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-15T12:44:42Z (GMT). No. of bitstreams: 1 ntu-105-R03221003-1.pdf: 966376 bytes, checksum: 1a1291c1a33a76cdf9630c65749a9060 (MD5) Previous issue date: 2016 | en |
| dc.description.tableofcontents | 1 Introduction.................................................................................. 1
2 Basic facts of G2 geometry........................................................ 2 2.1 Definitions of G2 geometry....................................................... 2 2.2 Classical results of G2 geometry............................................. 4 2.3 Reproof of some known facts.................................................. 6 2.4 Nearly parallel G2-structure...................................................... 15 3 Some volume functional on 7-manifold with G2-structure.... 18 3.1 Hithcin’s volume functional...................................................... 18 3.2 Grigorian’s volume functional................................................... 24 4 Definite connection on 4-dimensional manifolds......................... 30 4.1 A construction of Einstein metric on certain principal bundle.. 30 5 Appendix....................................................................................... 37 6 References.................................................................................... 47 | |
| dc.language.iso | en | |
| dc.subject | 幾乎平行 G2 結構 | zh_TW |
| dc.subject | 里奇曲率張量 | zh_TW |
| dc.subject | 愛因斯坦點積 | zh_TW |
| dc.subject | G2 流形 | zh_TW |
| dc.subject | 主叢 | zh_TW |
| dc.subject | Ricci curvature | en |
| dc.subject | Einstein metric | en |
| dc.subject | G2 manifold | en |
| dc.subject | principal bundle | en |
| dc.subject | nearly parallel G2-structure | en |
| dc.title | G2流形上的幾何性質 | zh_TW |
| dc.title | On the Geometry of G2 Manifolds | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 104-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 王慕道(Mu-Tao Wang),崔茂培(Mao-Pei Tsui) | |
| dc.subject.keyword | G2 流形,愛因斯坦點積,里奇曲率張量,主叢,幾乎平行 G2 結構, | zh_TW |
| dc.subject.keyword | G2 manifold,Einstein metric,Ricci curvature,principal bundle,nearly parallel G2-structure, | en |
| dc.relation.page | 48 | |
| dc.identifier.doi | 10.6342/NTU201601276 | |
| dc.rights.note | 有償授權 | |
| dc.date.accepted | 2016-07-26 | |
| 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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