Kähler Yamabe minimizers on minimal ruled surfaces - Tønnesen-Friedman, Christina W. (Mathematica Scandinavica, 2002)
It is shown that if a minimal ruled surface $P(E) → Σ$ admits a Kähler Yamabe minimizer, then this metric is generalized Kähler-Einstein and the holomorphic vector bundle $E$ is quasi-stable.