P Gilkey and S Nikčević 2004 Class. Quantum Grav. 21 497 doi:10.1088/0264-9381/21/2/013
Curvature homogeneous spacelike Jordan Osserman pseudo-Riemannian manifolds
P Gilkey1 and S Nikčević2
Show affiliationsLet s ≥ 2. We construct Ricci flat pseudo-Riemannian manifolds of signature (2s, s) which are not locally homogeneous but whose curvature tensors nevertheless exhibit a number of important symmetry properties. They are curvature homogeneous; their curvature tensor is modelled 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 ≤ k ≤ s; they are k-timelike higher-order Jordan Osserman for s + 2 ≤ k ≤ 2s, and they are not k-timelike higher-order Jordan Osserman for 2 ≤ k ≤ s + 1.
- PACS
- MSC
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47B36 Jacobi (tridiagonal) operators (matrices) and generalizations
53C35 Symmetric spaces (See also 32M15, 57T15)
53C30 Homogeneous manifolds (See also 14M15, 14M17, 32M10, 57T15)
- Subjects
- Dates
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Issue 2 (21 January 2004)
Received 2 October 2003
Published 10 December 2003
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Curvature homogeneous spacelike Jordan Osserman pseudo-Riemannian manifolds
P Gilkey and S Nikčević 2004 Class. Quantum Grav. 21 497
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