We consider pseudo-Riemannian generalizations of Osserman, Clifford, and the duality principle properties for algebraic curvature tensors and investigate relations between them. We introduce quasi-Clifford curvature tensors using a generalized Clifford family and show that they are Osserman. This allows us to discover an Osserman curvature tensor that does not satisfy the duality principle. We give some necessary and some sufficient conditions for the total duality principle. n i=1 ε Ei R(Y, X, X, E i )E i . The Jacobi operator is a self-adjoint endomorphism on V, and therefore it is diagonalizable if g is definite. However, this is no longer true in the indefinite setting, so if J X is diagonalizable for any nonnull X we say that R is Jacobi-diagonalizable. In general, the eigen-structure of J X is determined by the Jordan normal form (the number and the sizes of the Jordan blocks).We say that R is timelike Osserman (or spacelike Osserman) if the characteristic polynomial of the Jacobi operator J X is independent of unit timelike (or spacelike) X ∈ V. We say that R is timelike Jordan-Osserman (or spacelike Jordan-Osserman) if the Jordan normal form of J X is independent of unit timelike (or spacelike) X. An algebraic curvature tensor is Osserman if it is both
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