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CODAZZI TENSORS WITH TWO EIGENVALUE FUNCTIONS.
- Source :
-
Proceedings of the American Mathematical Society . Sep2013, Vol. 141 Issue 9, p3265-3273. 9p. - Publication Year :
- 2013
-
Abstract
- This paper addresses a gap in the classification 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 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 claim by A. L. Besse that the warped product conclusion holds without any restriction on the trace. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00029939
- Volume :
- 141
- Issue :
- 9
- Database :
- Academic Search Index
- Journal :
- Proceedings of the American Mathematical Society
- Publication Type :
- Academic Journal
- Accession number :
- 88426230
- Full Text :
- https://doi.org/10.1090/S0002-9939-2013-11616-3