Title: Infinitesimal Maximal Symmetry and Homogeneous Expanding
Ricci Solitons
Abstract: We address the following questions: Among all
left-invariant Riemannian metrics on a given Lie group, do there exist
metrics of maximal symmetry, i.e., metrics whose isometry groups
contain the isometry groups of all other left-invariant metrics? If
so, are those metrics with the ``nicest'' curvature properties
maximally symmetric? We find that left-invariant Einstein metrics of
negative Ricci curvature are maximally symmetric. Left-invariant
expanding Ricci solitons exhibit a weaker notion of ``infinitesimal''
maximal symmetry but are not always maximally symmetric.