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Jordan Szabo algebraic covariant derivative curvature tensors
Peter B. Gilkey, Raina Ivanova and Iva Stavrov
We show that if $\nabla R$ is a Jordan Szabo algebraic covariant derivative curvature tensor on a vector space of signature (p,q) where q is odd and p is less than q or where q is congruent to 2 mod 4 and p is less than q-1, then $\nabla R$ vanishes. This algebraic result yields an elementary proof of the geometric fact that any pointwise totally isotropic pseudo-Riemannian manifold with such a signature (p,q) is locally symmetric