Riemannian Metrics

  • Peter Petersen
Part of the Graduate Texts in Mathematics book series (GTM, volume 171)


In this chapter we introduce the spaces and maps that pervade the subject. Without discussing any theory we present several examples of basic Riemannian manifolds and Riemannian maps. All of these examples will be at the heart of future investigations into constructions of Riemannian manifolds with various interesting properties.


Unique Riemannian Metric Riemannian Base Manifold Constant Curvature Geometry Warped Product Coordinate Vector Fields 
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Copyright information

© Springer International Publishing AG 2016

Authors and Affiliations

  • Peter Petersen
    • 1
  1. 1.Department of MathematicsUniversity of California, Los AngelesLos AngelesUSA

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