Low dimensional Solsolitons

WILL, CYNTHIA

Congreso; III Congreso Latinoamericano de Geometría en Grupos de Lie; 2010

A complete Riemannian metric g on a differentiable manifold M is said to be aRicci soliton if its Ricci tensor satisfiesRc(g) = c g + LX g,  c ∈ R, X ∈ χ(M ) complete,where LX denotes the Lie derivative in the direction of the vector field X. Riccisolitons metrics came up in the study of the Ricci flow since they are precisely thefixed points of the flow up to isometry and scaling. In this talk, we will considerhomogeneous Ricci soliton metrics on simply connected solvable Lie groups, socalled solsolitons. Up to now, these are the only known examples of homogeneousnontrivial Ricci solitons metrics. Following the characterization given recently byLauret, we start with the already known classification of nilsolitons and formthere we get all solsolitons of dimension less or equal than 7.