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The Model Spaces Mκn

  • Martin R. Bridson
  • André Haefliger
Part of the Grundlehren der mathematischen Wissenschaften book series (GL, volume 319)

Abstract

In this chapter we shall construct the metric spaces M κ n , which play a central role in later chapters, serving as standard models to which one can profitably compare more general geodesic spaces. One way to describe M κ n is as the complete, simply connected, Riemannian n-manifold of constant sectional curvature κ ∈ ℝ. However, in keeping with the spirit of this book, we shall first define and study the M κ n purely as metric spaces (cf. [Iv92]), and defer consideration of their Riemannian structure until Chapter 6.

Keywords

Model Space Triangle Inequality Initial Vector Vector Subspace Geodesic Segment 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Martin R. Bridson
    • 1
  • André Haefliger
    • 2
  1. 1.Mathematical InstituteUniversity of OxfodOxfordGreat Britain
  2. 2.Section de MathématiquesUniversité de GenèveGenève 24Switzerland

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