Vol. 8, No. 2, 2015

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ISSN: 1948-206X (e-only)
ISSN: 2157-5045 (print)
Locally conformally flat ancient Ricci flows

Giovanni Catino, Carlo Mantegazza and Lorenzo Mazzieri

Vol. 8 (2015), No. 2, 365–371
Abstract

We show that any locally conformally flat ancient solution to the Ricci flow must be rotationally symmetric. As a by-product, we prove that any locally conformally flat Ricci soliton is a gradient soliton in the shrinking and steady cases as well as in the expanding case, provided the soliton has nonnegative curvature.

Keywords
Ricci solitons, Ricci flow
Mathematical Subject Classification 2010
Primary: 53C24, 53C25, 53C44
Milestones
Received: 8 May 2014
Accepted: 9 February 2015
Published: 10 May 2015
Authors
Giovanni Catino
Dipartimento di Matematica
Politecnico di Milano
Piazza Leonardo da Vinci 32
I-20133 Milano
Italy
Carlo Mantegazza
Scuola Normale Superiore di Pisa
Piazza dei Cavalieri 7
I-56126 Pisa
Italy
Lorenzo Mazzieri
Scuola Normale Superiore di Pisa
Piazza dei Cavalieri 7
I-56126 Pisa
Italy