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arXiv · 0804.0436

Four-dimensional Osserman metrics of neutral signature

E. Garcia-Rio·P. Gilkey·M. E. Vazquez-Abal·R. Vazquez-Lorenzo
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Abstract

In the algebraic context, we show that null Osserman, spacelike Osserman, and timelike Osserman are equivalent conditions for a model of signature (2,2). We also classify the null Jordan Osserman models of signature (2,2). In the geometric context, we show that a pseudo-Riemannian manifold of signature (2,2) is null Jordan Osserman if and only if either it has constant sectional curvature or it is locally a complex space form.

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E. Garcia-Rio, P. Gilkey, M. E. Vazquez-Abal, R. Vazquez-Lorenzo. 2008-04-02. Four-dimensional Osserman metrics of neutral signature. https://arxiv.org/abs/0804.0436

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