Geometry and topology of complex hyperbolic and CR-manifolds

Details Geometry and topology of complex hyperbolic and CR-manifolds Geometry and topology of complex hyperbolic and CR-manifolds

1997-01-26

arxiv.org/abs/math/9701212v1

Mathematics

Differential Geometry

Scientific paper

We study geometry, topology and deformation spaces of noncompact complex hyperbolic manifolds (geometrically finite, with variable negative curvature), whose properties make them surprisingly different from real hyperbolic manifolds with constant negative curvature. This study uses an interaction between K\"ahler geometry of the complex hyperbolic space and the contact structure at its infinity (the one-point compactification of the Heisenberg group), in particular an established structural theorem for discrete group actions on nilpotent Lie groups.

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