Higher-dimensional Osserman metrics with non-nilpotent Jacobi operators

2010/07/15 by E. Calvino-Louzao, Calvino-Louzao, E., Eduardo García‐Río +8
Mathematics · #53B30 #53C50 #Advanced Algebra and Geometry #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #math.DG #msc:53B30 #msc:53C50

paper · pdf · doi:10.48550/arxiv.1007.2569

arxiv created 2010/07/15 · openalex publication_date 2010/07/15 · arxiv updated 2010/07/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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• Four-dimensional Osserman metrics with nondiagonalizable Jacobi operators
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