On Calabi extremal Kähler-Ricci solitons

Calamai, Simone; Petrecca, David

doi:10.1090/proc12725

On Calabi extremal Kähler-Ricci solitons
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by Simone Calamai and David Petrecca PDF

Proc. Amer. Math. Soc. 144 (2016), 813-821 Request permission

Abstract:

In this note we give a characterization of Kähler metrics which are both Calabi extremal and Kähler-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.

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