Abstract
In this chapter we shall construct the metric spaces M n κ , 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 n κ 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 n κ purely as metric spaces (cf. [Iv92]), and defer consideration of their Riemannian structure until Chapter 6.
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© 1999 Springer-Verlag Berlin Heidelberg
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Bridson, M.R., Haefliger, A. (1999). The Model Spaces M n κ . In: Metric Spaces of Non-Positive Curvature. Grundlehren der mathematischen Wissenschaften, vol 319. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-12494-9_2
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DOI: https://doi.org/10.1007/978-3-662-12494-9_2
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-08399-0
Online ISBN: 978-3-662-12494-9
eBook Packages: Springer Book Archive