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Definitions and Examples of Riemannian Metrics

  • John M. Lee
Part of the Graduate Texts in Mathematics book series (GTM, volume 176)

Abstract

In this chapter we officially define Riemannian metrics and construct some of the elementary objects associated with them. At the end of the chapter, we introduce three classes of highly symmetric “model” Riemannian manifolds—Euclidean spaces, spheres, and hyperbolic spaces—to which we will return repeatedly as our understanding deepens and our tools become more sophisticated.

Keywords

Riemannian Manifold Hyperbolic Space Riemannian Geometry Stereographic Projection Riemannian Metrics 
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 New York, Inc. 1997

Authors and Affiliations

  • John M. Lee
    • 1
  1. 1.Department of MathematicsUniversity of WashingtonSeattleUSA

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