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Unformatted text preview: 1. R i jkl =-R i jlk 2. R i jkl =-R jikl 3. R i jkl = R kli j 4. R i [ jkl ] = R i jkl + R i kl j + R i l jk = 5. R i j = R ji Proof : 1. Theorem 6.2.3 The Weyl tensor has the same symmetry properties as the Riemann tensor and all its contractions vanish, that is, C i jik = . Proof : 1. Theorem 6.2.4 The number of algebraically independent components of the Riemann tensor of the Levi-Civita connection is equal to n 2 ( n 2-1) 12 . Proof : 1. di geom.tex; April 12, 2006; 17:59; p. 153...
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- Spring '10