ICTP Mathematics Seminar on Monday 18 March

[math]

M A T H E M A T I C S   S E M I N A R S   2013


Monday, 18 March, at 14.30 hrs.


Dr. Ernani Ribeiro Jr.
(Universidade do Ceara', Brazil)

"Some characterizations for compact almost Ricci solitons"


Abstract:

The study of an almost Ricci soliton was introduced in a recent paper 
due to Pigola, Rigoli, Rimoldi and Setti. This structure represents a 
generalization to Einstein metrics and Ricci soliton, they appear as 
special solutions of the Ricci flow. In this seminar we shall talk about 
two results. The first treats of the characterization of compact almost 
Ricci solitons , more precisely, in this work we find some structure 
equations for almost Ricci solitons which generalize the equivalent for 
Ricci solitons. As a consequence of these
equations we derive an integral formula for the compact case which 
enables to show that a compact nontrivial almost Ricci soliton is 
isometric to a sphere, provided either it has constant scalar curvature 
or its associated vector eld is conformal. Next, we prove that any 
compact almost Ricci soliton with constant scalar curvature is isometric 
to a Euclidean sphere. As a consequence we obtain that every compact 
almost Ricci soliton with constant scalar curvature is gradient.

VENUE: Luigi Stasi Seminar Room, first floor , ICTP Leonardo Building