Year: 2011
Type: preprint
Abstract: This paper addresses a gap in the classifcation of Codazzi tensors with exactly two eigenfunctions on a Riemannian manifold of dimension three or higher. Derdzinski proved that if the trace of such a tensor is constant and the dimension of one of the the eigenspaces is $n-1$, then the metric is a warped product where the base is an open interval- a conclusion we will show to be true under a milder trace condition. Furthermore, we construct examples of Codazzi tensors having two eigenvalue functions, one of which has eigenspace dimension $n-1$, where the metric is not a warped product with interval base, refuting a remark in \cite{Besse} that the warped product conclusion holds without any restriction on the trace.
Source: arXiv (Cornell University)
Author: Merton, Gabe
Institution: University of California, Los Angeles
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2952398935