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.
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.
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
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