Complex Hyperbolic Geometry (Hardcover)

William M. Goldman

ISBN 10: 019853793X / ISBN 13: 9780198537939

Editore: Oxford University Press, Oxford, 1999

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Hardcover. 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. Thisbook 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 spacesand discrete groups, it is designed to provide an introduction to this fascinating and important area and invite further research and development. The geometry of complex hyperbolic space has not, so far, been given a comprehensive treatment in the literature. This book seeks to address this by providing an overview of this particularly rich area of research, and is largely motivated by the wide applications in other areas of mathematics and physics. Shipping may be from our UK warehouse or from our Australian or US warehouses, depending on stock availability. Codice articolo 9780198537939

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Titolo: Complex Hyperbolic Geometry (Hardcover)

Casa editrice: Oxford University Press, Oxford

Data di pubblicazione: 1999

Legatura: Hardcover

Condizione: new

Descrizione articolo

Riassunto:

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.

Contenuti:

• 1: The complex projective line
• 2: Algebraic and geometric background
• 3: The ball model
• 4: The paraboloid model and Heisenberg geometry
• 5: Bisectors and spinal spheres
• 6: Automorphisms
• 7: Numerical invariants
• 8: Extors in projective space
• 9: Intersections of bisectorsAppendixBibliographyIndex
• Appendix
• Bibliography
• Index