Tamaru's WEB PAGE $B!d(B
Data of a talk
It is an important problem to examine whether a given Lie group admit
distinguished left-invariant metrics,
such as Einstein or Ricci soliton metrics.
In this talk, I will explain our approach from submanifold geometry.
In particular, for three-dimensional solvable Lie groups,
the existence and nonexistence of left-invariant Ricci soliton metrics
have a nice correspondence with the geometry of cohomogeneity one actions on some noncompact symmetric space.
I will also mention some higher-dimensional examples and a pseudo-Riemannian version.