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# Higher-dimensional Osserman metrics with non-nilpotent Jacobi operators

• ##### P. Gilkey
Geometriae Dedicata (Impact Factor: 0.47). 07/2010; DOI: 10.1007/s10711-011-9595-y
Source: arXiv

ABSTRACT We exhibit Osserman metrics with non-nilpotent Jacobi operators and with non-trivial Jordan normal form in neutral signature (n,n) for any n which is at least 3. These examples admit a natural almost para-Hermitian structure and are semi para-complex Osserman with non-trivial Jordan normal form as well; they neither satisfy the third Gray identity nor are they integrable.

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