Definitions and Examples of Riemannian Metrics

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


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.


Riemannian Manifold Hyperbolic Space Riemannian Geometry Stereographic Projection Riemannian Metrics 
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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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