25 jan 2012 -- 17:00
Sala Seminari, Department of Mathematics, University of Pisa
Einstein solitons are self-similar solutions to the geometric flow
dgdt = - 2 Ric + R g ,
where Ric and R are respectively the Ricci tensor and the scalar curvature of the metric g. A gradient Einstein soliton corresponds to a Riemannian manifold (M,g) such that there exists a smooth function f satisfying
Ric - (R2) g + Hess(f) = c g,
for some real number c. We will prove that if grad(f) is not parallel (in which case the soliton is trivial), then there exists a real function h such that f(p) = h(r(p)), where r is the signed distance to a fixed regular level set of f. When this happens, the soliton is said to be rectifiable. In the second part of the seminar we will present some of the geometric consequences of the rectifiability.