Higher-dimensional Osserman metrics with non-nilpotent Jacobi operators

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

2010-07-15

arxiv.org/abs/1007.2569v1

Mathematics

Differential Geometry

Scientific paper

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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