Codazzi tensors with two eigenvalue functions (Q2845475)
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scientific article; zbMATH DE number 6203454
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Codazzi tensors with two eigenvalue functions |
scientific article; zbMATH DE number 6203454 |
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Codazzi tensors with two eigenvalue functions (English)
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30 August 2013
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Codazzi tensor
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Riemannian manifold
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0.8909214
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0.88553625
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0.8802179
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The author ``addresses a gap in the classification of Codazzi tensors with exactly two eigenfunctions on a Riemannian manifold of dimension three or higher.'' NEWLINENEWLINENEWLINEFirst, he improves a result by Derdzinski, who proved that ``if the trace of a Codazzi tensor is constant and the dimension of one of the eigenspaces is \(n-1\), then the metric is a warped product, where the base is an open interval''.NEWLINENEWLINEMoreover, the author exhibits examples of Codazzi tensors which disprove a claim by A. L. Besse that the ``warped product conclusion holds without any restriction on the trace.''
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