## Peter Gilkey, Raina Ivanova

*The Jordan normal form of higher order Osserman algebraic curvature tensors *

Comment.Math.Univ.Carolinae 43,2 (2002) 231-242. **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

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