

Preprint 97/2002
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