The Jordan normal form of higher order Osserman algebraic curvature tensors

الأصل · EN

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.