Curvature homogeneous spacelike Jordan Osserman pseudo-Riemannian manifolds

Details Curvature homogeneous spacelike Jordan Osserman pseudo-Riemannian manifolds Curvature homogeneous spacelike Jordan Osserman pseudo-Riemannian manifolds

2003-10-02

arxiv.org/abs/math/0310024v2

Mathematics

Differential Geometry

Update bibliography, fix minor misprints

Scientific paper

10.1088/0264-9381/21/2/013

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

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