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Higher order Jordan Osserman Pseudo-Riemannian manifolds

Peter B. Gilkey·Raina Ivanova·Tan Zhang
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Abstract

We study the higher order Jacobi operator in pseudo-Riemannian geometry. We exhibit a family of manifolds so that this operator has constant Jordan normal form on the Grassmannian of subspaces of signature (r,s) for certain values of (r,s). These pseudo-Riemannian manifolds are new and non-trivial examples of higher order Osserman manifolds.

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Peter B. Gilkey, Raina Ivanova, Tan Zhang. 2002-07-10. Higher order Jordan Osserman Pseudo-Riemannian manifolds. https://doi.org/10.1088/0264-9381%2F19%2F17%2F306

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