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.
KeywordsRiemannian Manifold Scalar Curvature Sectional Curvature Curvature Tensor Curvature Operator
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