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Curvature

  • Peter Petersen
Chapter
  • 7.7k Downloads
Part of the Graduate Texts in Mathematics book series (GTM, volume 171)

Abstract

The idea of a Riemannian metric having curvature, while intuitively appealing and natural, is also often the stumbling block for further progress into the realm of geometry. The most elementary way of defining curvature is to set it up as an integrability condition. This indicates that when it vanishes it should be possible to solve certain differential equations, e.g., that the metric is Euclidean. This was in fact one of Riemann’s key insights.

Keywords

Jacobi Field Warped Product Metric Einstein Constant Smooth Distance Function Curvature Tensor 
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.

Bibliography

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    M. Spivak, A Comprehensive Introduction to Differential Geometry, vol. I-V (Publish or Perish, Wilmington, 1979)Google Scholar

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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