Szabo Osserman IP Pseudo-Riemannian manifolds

Mathematics – Differential Geometry

Scientific paper

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Scientific paper

We construct a family of pseudo-Riemannian manifolds so that the
skew-symmetric curvature operator, the Jacobi operator, and the Szabo operator
have constant eigenvalues on their domains of definition. This provides new and
non-trivial examples of Osserman, Szabo, and IP manifolds. We also study when
the associated Jordan normal form of these operators is constant.

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