Higher-dimensional Osserman metrics with non-nilpotent Jacobi operators |
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| Authors: | E Calviño-Louzao E García-Río P Gilkey R Vázquez-Lorenzo |
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| Institution: | (1) Dept. of Geometry and Topology, Faculty of Mathematics, Univ. of Santiago de Compostela, 15782 Santiago, Spain;(2) Dept. of Mathematics, Atilim University, Incek, 06836 Ankara, Turkey |
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| 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 ≥ 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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