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


We are now ready to compute the covariant derivative and curvature tensors on the examples we constructed earlier. After computing these quantities in general, we will try to find examples of manifolds with constant sectional, Ricci, and scalar curvature. In particular, we shall look at the standard product metrics on spheres and also construct the Riemannian version of the Schwarzschild metric.


Riemannian Manifold Scalar Curvature Sectional Curvature Curvature Tensor Curvature Operator 
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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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