We introduce a natural extension of the concept of gradient Ricci soliton: the Ricci almost soliton. We provide existence and rigidity results, we deduce a-priori curvature estimates and isolation phenomena, and we investigate some topological properties. A number of differential identities involving the relevant geometric quantities are derived. Some basic tools from the weighted manifold theory such as general weighted volume comparisons and maximum principles at infinity for diffusion operators are discussed

Pigola, S., Rigoli, M., Rimoldi, M., Setti, A. (2011). Ricci almost solitons. ANNALI DELLA SCUOLA NORMALE SUPERIORE DI PISA. CLASSE DI SCIENZE, 10(4), 757-799 [10.2422/2036-2145.2011.4.01].

Ricci almost solitons

Pigola, S;RIMOLDI, MICHELE;
2011

Abstract

We introduce a natural extension of the concept of gradient Ricci soliton: the Ricci almost soliton. We provide existence and rigidity results, we deduce a-priori curvature estimates and isolation phenomena, and we investigate some topological properties. A number of differential identities involving the relevant geometric quantities are derived. Some basic tools from the weighted manifold theory such as general weighted volume comparisons and maximum principles at infinity for diffusion operators are discussed
Articolo in rivista - Articolo scientifico
Mathematics
English
2011
10
4
757
799
none
Pigola, S., Rigoli, M., Rimoldi, M., Setti, A. (2011). Ricci almost solitons. ANNALI DELLA SCUOLA NORMALE SUPERIORE DI PISA. CLASSE DI SCIENZE, 10(4), 757-799 [10.2422/2036-2145.2011.4.01].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/64613
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