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Unformatted text preview: These identities are called the Bianci identities . Proof : 1. di 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 Rie-mann tensor, R i j kl = m m R i j kl . di geom.tex; April 12, 2006; 17:59; p. 155...
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