Abstract
In complex hyperbolic geometry we consider an open set biholomorphic to an open ball in Cn, and we equip it with a particular metric that makes it have constant negative holomorphic curvature. This is analogous to but different from the real hyperbolic space. In the complex case, the sectional curvature is constant on complex lines, but it changes when we consider real 2-planes which are not complex lines.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer Basel
About this chapter
Cite this chapter
Cano, A., Navarrete, J.P., Seade, J. (2013). Complex Hyperbolic Geometry. In: Complex Kleinian Groups. Progress in Mathematics, vol 303. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-0481-3_2
Download citation
DOI: https://doi.org/10.1007/978-3-0348-0481-3_2
Published:
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-0480-6
Online ISBN: 978-3-0348-0481-3
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)