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Unformatted text preview: These identities are called the Bianci identities . Proof : 1. di ﬀ geom.tex; April 12, 2006; 17:59; p. 154 156 CHAPTER 6. CONNECTION AND CURVATURE ± • Corollary 6.2.4 The divergences of the Riemann tensor and the Ricci tensor have the form ∇ i R i j kl = ∇ k R j l ∇ l R j k , ∇ i R i j = 1 2 ∇ j R . The divergence of the Einstein tensor vanishes ∇ i G i j = . Proof : 1. ± • Problem. By using the Bianci identities simplify the Laplacian of the Riemann tensor, Δ R i j kl = ∇ m ∇ m R i j kl . di ﬀ geom.tex; April 12, 2006; 17:59; p. 155...
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 Spring '10
 Wong
 Geometry, Scalar, General Relativity, Riemannian geometry, Riemann curvature tensor, Riemann tensor, Bianci Identities

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