We discuss a gap in Besse’s book (Einstein manifolds, 2008), recently pointed out by Merton in (Proc Am Math Soc 141:3265–3273, 2013), 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.
A note on Codazzi tensors / Catino, Giovanni; Mantegazza, Carlo; Mazzieri, Lorenzo. - In: MATHEMATISCHE ANNALEN. - ISSN 0025-5831. - 362:1-2(2015), pp. 629-638. [10.1007/s00208-014-1135-2]
A note on Codazzi tensors
Mazzieri, Lorenzo
2015-01-01
Abstract
We discuss a gap in Besse’s book (Einstein manifolds, 2008), recently pointed out by Merton in (Proc Am Math Soc 141:3265–3273, 2013), 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.File | Dimensione | Formato | |
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