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Higher order Ossermann pseudo-Riemannian manifolds of neutral signature \((2, 2)\). (English) Zbl 1092.53053
Summary: We construct a family of pseudo-Riemannian metrics of neutral signature \((2,2)\) which leads to \(k\)-Osserman manifolds for all admissible \(k\). For these manifolds the generalized Jacobi operator is 2-nilpotent. Conditions for local symmetry on the considered manifolds are established.
MSC:
53C50 Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics
53C35 Differential geometry of symmetric spaces
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