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Higher-dimensional Osserman metrics with non-nilpotent Jacobi operators

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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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Authors and Affiliations

  1. Department of Geometry and Topology, Faculty of Mathematics, University of Santiago de Compostela, 15782, Santiago de Compostela, Spain

    E. Calviño-Louzao, E. García-Río & R. Vázquez-Lorenzo

  2. Mathematics Department, University of Oregon, Eugene, OR, 97403, USA

    P. Gilkey

Authors
  1. E. Calviño-Louzao
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  2. E. García-Río
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  3. P. Gilkey
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  4. R. Vázquez-Lorenzo
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Correspondence to E. García-Río.

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Calviño-Louzao, E., García-Río, E., Gilkey, P. et al. Higher-dimensional Osserman metrics with non-nilpotent Jacobi operators. Geom Dedicata 156, 151–163 (2012). https://doi.org/10.1007/s10711-011-9595-y

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  • DOI: https://doi.org/10.1007/s10711-011-9595-y

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