Codazzi tensors with two eigenvalue functions
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.''
scientific article; zbMATH DE number 6203454
scientific article