Infinitesimal Maximal Symmetry and Homogeneous Expanding
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.
This is joint work with Michael Jablonski.