Curvature tensors and covariant derivatives

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The problems considered here are of two types.(i) What are implications of vanishing k-th covariant derivatives of curvature tensors?(ii) Under what conditions on curvature tensors, does the k-th covariant derivative ∇kT=0 for a tensor T mean ∇T=0?


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Entrato in Redazione il 16 Maggio 1972.

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Tanno, S. Curvature tensors and covariant derivatives. Annali di Matematica 96, 233 (1973) doi:10.1007/BF02414842

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  • Covariant Derivative
  • Curvature Tensor