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MiS Preprint
97/2002

Jordan Szabo algebraic covariant derivative curvature tensors

Peter B. Gilkey, Raina Ivanova and Iva Stavrov

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 where q is congruent to 2 mod 4 and p is less than q-1, then ∇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

Contact the author per mail Download full preprint 207 KB
Received:
05.11.02
Published:
05.11.02
MSC Codes:
53B20
Keywords:
szabo tensor, totally isotropic manifold

Related publications

inBook
2003 Repository Open Access
Peter B. Gilkey, Raina Ivanova and Iva Stavrov

Jordan Szabo algebraic covariant derivative curvature tensors

In: Recent advances in Riemannian and Lorentzian geometries / Krishnan L. Duggal (ed.)
Providence, RI : American Mathematical Society, 2003. - pp. 65-75
(Contemporary mathematics ; 337)
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