曲面几何学 英文版PDF格式文档图书下载
- 购买点数:10 点
- 作 者:JohnStillwell著
- 出 版 社:世界图书北京出版公司
- 出版年份:2010
- ISBN:9787510005312
- 标注页数:216 页
- PDF页数:230 页
Chapter 1.The Euclidean Plane 1
1.1 Approaches to Euclidean Geometry 1
1.2 Isometries 2
1.3 Rotations and Reflections 5
1.4 The Three Reflections Theorem 9
1.5 Orientation-Reversing Isometries 11
1.6 Distinctive Features of Euclidean Geometry 14
1.7 Discussion 18
Chapter 2.Euclidean Surfaces 21
2.1 Euclid on Manifolds 21
2.2 The Cylinder 22
2.3 The Twisted Cylinder 25
2.4 The Torus and the Klein Bottle 26
2.5 Quotient Surfaces 29
2.6 A Nondiscontinuous Group 33
2.7 Euclidean Surfaces 34
2.8 Covering a Surface by the Plane 36
2.9 The Covering Isometry Group 39
2.10 Discussion 41
Chapter 3.The Sphere 45
3.1 The Sphere S2 in R3 45
3.2 Rotations 48
3.3 Stereographic Projection 50
3.4 Inversion and the Complex Coordinate on the Sphere 52
3.5 Reflections and Rotations as Complex Functions 56
3.6 The Antipodal Map and the Elliptic Plane 60
3.7 Remarks on Groups,Spheres and Projective Spaces 63
3.8 The Area of a Triangle 65
3.9 The Regular Polyhedra 67
3.10 Discussion 69
Chapter 4.The Hyperbolic Plane 75
4.1 Negative Curvature and the Half-Plane 75
4.2 The Half-Plane Model and the Conformal Disc Model 80
4.3 The Three Reflections Theorem 85
4.4 Isometries as Complex Functions 88
4.5 Geometric Description of Isometries 92
4.6 Classification of Isometries 96
4.7 The Area of a Triangle 99
4.8 The Projective Disc Model 101
4.9 Hyperbolic Space 105
4.10 Discussion 108
Chapter 5.Hyperbolic Surfaces 111
5.1 Hyperbolic Surfaces and the Killing-Hopf Theorem 111
5.2 The Pseudosphere 112
5.3 The Punctured Sphere 113
5.4 Dense Lines on the Punctured Sphere 118
5.5 General Construction of Hyperbolic Surfaces from Polygons 122
5.6 Geometric Realization of Compact Surfaces 126
5.7 Completeness of Compact Geometric Surfaces 129
5.8 Compact Hyperbolic Surfaces 130
5.9 Discussion 132
Chapter 6.Paths and Geodesics 135
6.1 Topological Classification of Surfaces 135
6.2 Geometric Classification of Surfaces 138
6.3 Paths and Homotopy 140
6.4 Lifting Paths and Lifting Homotopies 143
6.5 The Fundamental Group 145
6.6 Generators and Relations for the Fundamental Group 147
6.7 Fundamental Group and Genus 153
6.8 Closed Geodesic Paths 154
6.9 Classification of Closed Geodesic Paths 156
6.10 Discussion 160
Chapter 7.Planar and Spherical Tessellations 163
7.1 Symmetric Tessellations 163
7.2 Conditions for a Polygon to Be a Fundamental Region 167
7.3 The Triangle Tessellations 172
7.4 Poincaré's Theorem for Compact Polygons 178
7.5 Discussion 182
Chapter 8.Tessellations of Compact Surfaces 185
8.1 Orbifolds and Desingularizations 185
8.2 From Desingularization to Symmetric Tessellation 189
8.3 Desingularizations as(Branched) Coverings 190
8.4 Some Methods of Desingularization 194
8.5 Reduction to a Permutation Problem 196
8.6 Solution of the Permutation Problem 198
8.7 Discussion 201
References 203
Index 207
- 《曲面几何学 英文版》JohnStillwell著 2010
- 《计算几何中的几何偏微分方程方法 英文版》徐国良,张琴著 2013
- 《微分几何基础 英文版》(美)Barrett ONeill 2009
- 《代数几何和算术曲线 英文》(德)刘青著 2012
- 《计算共形几何 英文版》顾险峰,丘成桐编著 2008
- 《微分几何 理论与应用 英文版》(法)希阿雷 2007
- 《曲面几何》(英)维舍本(Charles Ernest Weatherburn)撰;周绍濂译 1951
- 《离散群几何 英文》(英)比尔登著 2011
- 《复杂曲面数字化制造的几何学理论和方法》丁汉,朱利民著 2011
- 《几何 3 曲面理论》Yu.d.Burago著 2009
- 《曲面几何学 英文版》JohnStillwell著 2010
- 《达摩出身传灯传》(明)朱开泰著;(清)佚名著;(清)醉月山人著 2001
- 《醋葫芦》(清)伏雌教主著;(清)无名氏著;(清)无名氏著 2000
- 《蜃楼志全传》(清)瘐岭劳人著;(清)佚名著;(明)嘉禾餐花主人著 1999
- 《锦绣衣》(清)无名氏著;(明)佚名著;(清)无名氏著 2000
- 《随园诗话 下》(清)袁枚著(南朝)钟嵘著(南朝梁)刘勰著(清)王国维著 2222
- 《为了告别的聚会》(捷克)米兰·昆德拉著;时正伟译;(前苏联)鲍里斯·皮利尼亚克著;刘丽译;(日)德田秋声著;严喜东译 2001
- 《金银花》王丽著;刘大会著;张智慧著;石亚娜著;杨雁等著;赵仁,张金渝编 2013
- 《醋葫芦》(清)伏雌教主著;(清)佚名著;(清)佚名著 2001
- 《霍比特人电影完全指南》NorlothElbereth著;列奥诺拉著;Mithrandir著;王菁著;丁秀群著;胡冬兰著;AlanLee插图作者,DarrellSweet插图作者,DavidWenzel插图作者 2013
- 《计算数论 第2版 世界图书出版公司》SONG Y.YAN著 2004
- 《儿子与情人》Notes by Lance St John Butler 1990
- 《自然密码》闫茂龙编著 2007
- 《世界图书出版与印刷博物馆》A.M.茨冈年科 2018
- 《北京大学图书馆藏善本书录 中英文本》张玉范,沈乃文主编 1998
- 《冰淇淋生产与配方》蔡云升著 1995
- 《投资北京全程指南 有限责任公司篇(2010-2011)》张龙,赵清主编 2010
- 《北京社科图书发行公司 11 200年历史类订书目录》 2222
- 《北京社科图书发行公司 8 200年文学类订书目录》 2222
- 《北京图书馆出版社图书总目 1979-1999》姜红编撰 1999