Tamaru's WEB PAGE $B!d(B
Left-invariant Riemannian metrics on Lie groups
have provided many interesting examples of homogeneous Einstein and Ricci soliton manifolds.
In general, it is not easy to examine whether a given Lie group admit such distinguished metrics or not.
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 solitons 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.