Jordan Szabo algebraic covariant derivative curvature tensors

Peter B. Gilkey, Raina Ivanova, and Iva Stavrov

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Submission date: 05. Nov. 2002
Pages: 13
published in: Recent advances in Riemannian and Lorentzian geometries / K. L. Duggal (ed.)
Providence, RI : American Mathematical Society, 2003. - P. 65 - 75
(Contemporary mathematics ; 337) 
Bibtex
MSC-Numbers: 53B20
Keywords and phrases: szabo tensor, totally isotropic manifold
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Abstract:
We show that if 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 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