Abstract:We construct new examples of algebraic curvature tensors so that the Jordan normal form of the higher order Jacobi operator is constant on the Grassmannian of subspaces of type $(r,s)$ in a vector space of signature $(p,q)$. We then use these examples to establish some results concerning higher order Osserman and higher order Jordan Osserman algebraic curvature tensors.
Keywords: higher order Jacobi operator, Osserman algebraic curvature tensors, Jordan Osserman algebraic curvature tensors
AMS Subject Classification: 53B20