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We study when the Jacobi operator associated to the Weyl confor-mal curvature tensor has constant eigenvalues on the bundle of unit spacelike or timelike tangent vectors. This leads to questions in the conformal geometry of pseudo-Riemannian manifolds which generalize the Osserman conjecture to this setting. We also study similar questions related to the(More)
There is a 14-dimensional algebraic curvature tensor which is Jacobi–Tsankov (i.e. J (x)J (y) = J (y)J (x) for all x, y) but which is not 2-step Jacobi nilpotent (i.e. J (x)J (y) = 0 for some x, y); the minimal dimension where this is possible is 14. We determine the group of symmetries of this tensor and show that it is geometrically realizable by a wide(More)
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