Codice  QDD201 
Titolo  Gradient Einstein solitons 
Data  20150326 
Autore/i  Catino, G.; Mazzieri, L. 
Link  Download full text 
Abstract  In this paper we consider a perturbation of the Ricci solitons equation proposed by J. P. Bourguignon. We show that these structures are more rigid then standard Ricci solitons. In particular, we prove that there is only one complete threedimensional, positively curved, Riemannian manifold satisfying $$ Ric \frac{1}{2} R g + \nabla2 f = 0 $$, for some smooth function $f$. This solution is rotationally symmetric and asymptotically cylindrical and it represents the analogue of the Hamilton's cigar in dimension three. The key ingredient in the proof is the rectifiability of the potential function $f$. It turns out that this property holds also in the Lorentzian setting and for a more general class of structures which includes some gravitational theories. 
