The contributions in this volume summarize parts of a seminar on conformal geometry which was held at the Max-Planck-Institut fur Mathematik in Bonn during the academic year 1985/86. The intention of this seminar was to study conformal structures on mani folds from various viewpoints. The motivation to publish seminar notes grew out of the fact that in spite of the basic importance of this field to many topics of current interest (low-dimensional topology, analysis on manifolds . . . ) there seems to be no coherent introduction to conformal geometry in the literature. We have tried to make the material presented in this book self-contained, so it should be accessible to students with some background in differential geometry. Moreover, we hope that it will be useful as a reference and as a source of inspiration for further research. Ravi Kulkarni/Ulrich Pinkall Conformal Structures and Mobius Structures Ravi S. Kulkarni* Contents § 0 Introduction 2 § 1 Conformal Structures 4 § 2 Conformal Change of a Metric, Mobius Structures 8 § 3 Liouville's Theorem 12 n §4 The GroupsM(n) andM(E ) 13 § 5 Connection with Hyperbol ic Geometry 16 § 6 Constructions of Mobius Manifolds 21 § 7 Development and Holonomy 31 § 8 Ideal Boundary, Classification of Mobius Structures 35 * Partially supported by the Max-Planck-Institut fur Mathematik, Bonn, and an NSF grant. 2 §O Introduction (0. 1) Historically, the stereographic projection and the Mercator projection must have appeared to mathematicians very startling.
This consumable book provides lesson support material for students to analyze and complete. It provides a long-term record of each student’s mathematical development.
A Course of Mathematics for Engineers and Scientists
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我国《周髀算经》一开始就记载了周朝初年(约公元前1100年左右)的周公与学者商高的对话,其中就谈到“勾三股四弦五”,即勾股定理的特殊形式;还记载了在周公之后的陈子,曾用勾股定理和相似图形的比例关系,推算过地球与太阳的距离和太阳的直径,同时为勾股定.
YOUR BRAIN+MATH>YOUR BRAIN-MATH 寫給每個人的數學讀本, 不管你是喜歡還是厭惡數學,都不能錯過這本書! 數學奇才布伊斯曼帶領讀者穿越歷史, 從兩河文明、古埃及、中國到現代, ...
Focuses on the successive construction and development of the basic number systems of mathematics: positive integers, integers, rational numbers, real numbers and complex numbers.
This is an advanced text for the one- or two-semester course in analysis taught primarily to math, science, computer science, and electrical engineering majors at the junior, senior or graduate...