Vol. 8, No. 2, 2015

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Locally conformally flat ancient Ricci flows

Giovanni Catino, Carlo Mantegazza and Lorenzo Mazzieri

Vol. 8 (2015), No. 2, 365–371

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.

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