#
*A study of homogeneous Einstein metrics*

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