Tamaru's WEB PAGE $B!d(B
Our theme is the geometry of left-invariant Riemannian metrics on Lie groups,
which provide many interesting examples of homogeneous Einstein and Ricci soliton manifolds.
In this talk, I will explain our approach from submanifold geometry.
In particular, for three-dimensional solvable Lie groups,
the existence and the nonexistence of left-invariant Ricci solitons have a nice correspondence
with geometry of cohomogeneity one actions on some noncompact symmetric space.
I will also mention some higher-dimensional examples and a pseudo-Riemannian version.