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Displaying similar documents to “The nonexistence of rank 4 IP tensors in signature ( 1 , 3 ) .”

The Jordan normal form of higher order Osserman algebraic curvature tensors

Peter Gilkey, Raina Ivanova (2002)

Commentationes Mathematicae Universitatis Carolinae

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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.