Higher order Jordan Osserman Pseudo-Riemannian manifolds

We study the higher order Jacobi operator in pseudo-Riemannian geometry. We exhibit a family of manifolds so that this operator has constant Jordan normal form on the Grassmannian of subspaces of signature (r,s) for certain values of (r,s). These pseudo-Riemannian manifolds are new and non-trivial e...

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Bibliographic Details
Published inarXiv.org
Main Authors Gilkey, Peter B, Ivanova, Raina, Zhang, Tan
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 10.07.2002
Subjects
Operators (mathematics)
Riemann manifold
Subspaces
Theorems
Topological manifolds
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Summary:We study the higher order Jacobi operator in pseudo-Riemannian geometry. We exhibit a family of manifolds so that this operator has constant Jordan normal form on the Grassmannian of subspaces of signature (r,s) for certain values of (r,s). These pseudo-Riemannian manifolds are new and non-trivial examples of higher order Osserman manifolds.
ISSN:2331-8422
DOI:10.48550/arxiv.0205269