Jordan Szabo algebraic covariant derivative curvature tensors

2002/11/05 by Peter B. Gilkey, Gilkey, Peter B., Raina Ivanova +3
Mathematics · #53B20 #Differential Geometry (math.DG) #FOS: Mathematics #math.DG #msc:53B20

paper · pdf · doi:10.48550/arxiv.math/0211089

arxiv created 2002/11/05 · arxiv updated 2009/11/30

Abstract

We show that if ∇ 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 if q is congruent to 2 mod 4 and if p is less than q-1, then ∇ R=0. This algebraic result yields an elementary proof of the geometrical fact that any pointwise totally isotropic pseudo-Riemannian manifold with such a signature (p,q) is locally symmetric.

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