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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
##### Keywords:
Jacobi operator; 2-nilpotent