English

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 2ks2\le k\le s; they are k-timelike higher order Jordan Osserman for s+2k2ss+2\le k\le 2s, and they are not k timelike higher order Jordan Osserman for 2ss+12\le s\le s+1.

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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}
}

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