Complex Hyperbolic Geometry

Hardcover | January 1, 1999

byWilliam M. Goldman

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Complex hyperbolic geometry is a particularly rich area of study, enhanced by the confluence of several areas of research including Riemannian geometry, complex analysis, symplectic and contact geometry, Lie group theory, and harmonic analysis. The boundary of complex hyperbolic geometry,known as spherical CR or Heisenberg geometry, is equally rich, and although there exist accounts of analysis in such spaces there is currently no account of their geometry. This book redresses the balance and provides an overview of the geometry of both the complex hyperbolic space and its boundary.Motivated by applications of the theory to geometric structures, moduli spaces and discrete groups, it is designed to provide an introduction to this fascinating and important area and invite further research and development.

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Complex hyperbolic geometry is a particularly rich area of study, enhanced by the confluence of several areas of research including Riemannian geometry, complex analysis, symplectic and contact geometry, Lie group theory, and harmonic analysis. The boundary of complex hyperbolic geometry,known as spherical CR or Heisenberg geometry, is...

William M. Goldman is at University of Maryland.

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Format:HardcoverPublished:January 1, 1999Publisher:Oxford University PressLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:019853793X

ISBN - 13:9780198537939

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Table of Contents

1. The complex projective line2. Algebraic and geometric background3. The ball model4. The paraboloid model and Heisenberg geometry5. Bisectors and spinal spheres6. Automorphisms7. Numerical invariants8. Extors in projective space9. Intersections of bisectorsAppendixBibliographyIndexAppendixBibliographyIndex

Editorial Reviews

"The book will be a useful reference tool for mathematicians and a helpful text for advanced students" Aslib Book Guide, August 1999