AbstractEinstein metrics can be characterised as critical points of the (normalised) total scalar curvature functional. They are always saddle points. However, there are Einstein metrics which are local maxima of the functional restricted to metrics of fixed volume and constant scalar curvature. These are by definition stable Einstein metrics. Stability can equivalently be characterised by a sp...
Abstract:(joint work with Rosa Sena-Dias) A theorem of Derdziński from the 1980's establishes that certain Einstein metrics are conformal to Bach-flat extremal Kahler metrics. Using this result Rosa Sena-Dias and I classified conformally Kähler, U(2)-invariant, Einstein metrics on the total space of O(−m). This yields infinitely many 1-parameter families of metrics exhibiting several differe...