Curvature homogeneous spacelike Jordan Osserman pseudo-Riemannian manifolds
Differential Geometry
2009-11-10 v2 Mathematical Physics
math.MP
Abstract
Let s be at least 2. We construct Ricci flat pseudo-Riemannian manifolds of signature (2s,s) which are not locally homogeneous but whose curvature tensors never the less exhibit a number of important symmetry properties. They are curvature homogeneous; their curvature tensor is modeled on that of a local symmetric space. They are spacelike Jordan Osserman with a Jacobi operator which is nilpotent of order 3; they are not timelike Jordan Osserman. They are k-spacelike higher order Jordan Osserman for ; they are k-timelike higher order Jordan Osserman for , and they are not k timelike higher order Jordan Osserman for .
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Cite
@article{arxiv.math/0310024,
title = {Curvature homogeneous spacelike Jordan Osserman pseudo-Riemannian manifolds},
author = {P. Gilkey and S. Nikcevic},
journal= {arXiv preprint arXiv:math/0310024},
year = {2009}
}
Comments
Update bibliography, fix minor misprints