dg/dt = - 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 - (R/2) 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.
When | Wed Jan 25, 2012 4pm – 5pm Coordinated Universal Time |
Where | Sala Seminari, Department of Mathematics, University of Pisa (map) |