On Calabi extremal Kaehler-Ricci solitons
  In this note we give a characterization of Kaehler metrics which are both Calabi extremal and Kaehler-Ricci solitons in terms of complex Hessians and the Riemann curvature tensor. We apply it to prove that, under the assumption of positivity of the holomorphic sectional curvature, these metrics are Einstein. 
Simone Calamai and David Petrecca
math.DG