A study of homogeneous Einstein metrics

Megan Kerr (Wellesley)

Given a homogeneous space G/H with G a compact simple Lie group and H a closed subgroup, when do we know there exist G-invariant Einstein metrics on G/H?  It is known that in this setting, there are some homogeneous spaces admitting several G-invariant Einstein metrics. And there are also some homogeneous spaces admitting no G-invariant Einstein metrics. It is still unknown whether such a homogeneous space can ever have a one-parameter family of (non-homothetic) G-invariant Einstein metrics.  Einstein metrics can be characterized as the critical points of the scalar curvature functional. We use this variational approach to derive the Einstein equations in the homogeneous setting G/H with G compact and simple.

Spring 2002 CTS/PNGS meeting