Calculus of Variations and Geometric Measure Theory

G. Catino - C. Mantegazza - L. Mazzieri

A Note on Codazzi Tensors

created by root on 15 May 2012
modified by catino on 12 May 2015


Published Paper

Inserted: 15 may 2012
Last Updated: 12 may 2015

Journal: Math. Ann.
Volume: 362
Number: 1-2
Pages: 629-638
Year: 2015


We discuss a gap in Besse's book, recently pointed out by Merton, which concerns the classification of Riemannian manifolds admitting a Codazzi tensors with exactly two distinct eigenvalues. For such manifolds, we prove a structure theorem, without adding extra hypotheses and then we conclude with some application of this theory to the classification of three-dimensional gradient Ricci solitons.