Time

Aug 28 2012 - 1:45pm - 2:45 pm

Location

CH 240

Speaker

Andrzej Derdzinski (OSU)

Abstract

The question of classifying homogeneous Einstein manifolds has so far been only partially answered. The special case of left-invariant Einstein metrics  on Lie groups seems equally vexing. This talk,  the first part of a two-talk sequence, concentrates  on the latter case. I will outline older existence  results of D'Atri and Ziller (1979) and more recent  progress made by Heber (1998) and Lauret (2010)  towards understanding the moduli and properties  of such metrics on solvable Lie groups. I also intend  to  introduce the more general classes of left- invariant "Einstein connections" and left-invariant  pseudo-Riemannian Einstein metrics. These classes  and new results about them will be the subject of  the second talk.