Curvature

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

Abstract

With the comforting feeling that there is indeed a variety of Riemannian manifolds out there, we shall now delve into the theory. Initially, we shall confine ourselves to infinitesimal considerations. The most important and often also least understood object of Riemannian geometry is that of the Riemannian connection. From this concept it will be possible to define curvature and more familiar items like gradients and Hessians of functions. Studying curvature is the central theme of Riemannian geometry. The idea of a Riemannian metric having curvature, while intuitively appealing and natural, is for most people the stumbling block for further progress into the realm of geometry.

Keywords

Vector Field Riemannian Manifold Distance Function Covariant Derivative Sectional Curvature 
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 Science+Business Media New York 1998

Authors and Affiliations

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

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