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

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

DOI: https://doi.org/10.1090/proc12725

Published electronically: June 26, 2015

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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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