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.
- ISBN10 3528089822
- ISBN13 9783528089825
- Publish Date 21 December 1988
- Publish Status Out of Print
- Out of Print 8 November 2009
- Publish Country DE
- Imprint Friedrich Vieweg & Sohn Verlagsgesellschaft mbH
- Edition 1988 ed.
- Format Paperback
- Pages 246
- Language English