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Examples of Conformally 2-Nilpotent Osserman Manifolds of Signature (2,2)*

Volume 9, Number 1 (2010), 96 - 103

Examples of Conformally 2-Nilpotent Osserman Manifolds of Signature (2,2)*

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Abstract

We exhibit pseudo-Riemannian metrics of signature (2, 2) which are conformally Osserman manifolds and geodesically complete. For these manifolds, the conformal Jacobi operator is 2-nilpotent. Conditions for being locally conformally symmetric on these manifolds are also established.