Delve into the future of research at MiS with our preprint repository. Our scientists are making groundbreaking discoveries and sharing their latest findings before they are published. Explore repository to stay up-to-date on the newest developments and breakthroughs.
MiS Preprint
97/2002
Jordan Szabo algebraic covariant derivative curvature tensors
Peter B. Gilkey, Raina Ivanova and Iva Stavrov
Abstract
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
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)