Some Other Invariant Metrics

  • Robert E. Greene
  • Kang-Tae Kim
  • Steven G. Krantz
Part of the Progress in Mathematics book series (PM, volume 291)


Chapters 3 and 4 explored extensively the use of the Bergman metric in studying the function theory of bounded domains and in particular their automorphism groups. The Bergman metric also played a role in Chapter 5 in the Bedford/Dadok proof of the realizability of every compact Lie group as an automorphism group. In all these instances, the invariance of the Bergman metric made it possible to bring to bear powerful differential geometric methods that would not have been otherwise available. But there are other invariant metrics that also deserve attention for their utility in such investigations. The purpose of this chapter is to give a quick survey of some of them.


Riemann Surface Sectional Curvature Complex Manifold Bergman Kernel Levi Form 
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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • Robert E. Greene
    • 1
  • Kang-Tae Kim
    • 2
  • Steven G. Krantz
    • 3
  1. 1.Department of MathematicsUniversity of CaliforniaLos AngelesUSA
  2. 2.Department of MathematicsPohang Institute of Science and TechnologyPohangSouth Korea
  3. 3.Department of MathematicsWashington UniversitySt. LouisUSA

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