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Proceedings of the American Mathematical Society

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On Calabi extremal Kähler-Ricci solitons

Authors: Simone Calamai and David Petrecca
Journal: Proc. Amer. Math. Soc. 144 (2016), 813-821
MSC (2010): Primary 53C25, 53C55
Published electronically: June 26, 2015
MathSciNet review: 3430856
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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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Additional Information

Simone Calamai
Affiliation: Dipartmento di Matematica e Informatica “U. Dini”, Università di Firenze, Viale Morgagni 67A, Firenze, Italy

David Petrecca
Affiliation: Institut für Differentialgeometrie, Leibniz Universität Hannover, Welfengarten 1, 30167, Hannover, Germany
MR Author ID: 985730

Keywords: Extremal Kähler metrics, Kähler-Ricci solitons, Einstein manifolds, holomorphic sectional curvature
Received by editor(s): May 19, 2014
Received by editor(s) in revised form: January 20, 2015
Published electronically: June 26, 2015
Communicated by: Lei Ni
Article copyright: © Copyright 2015 American Mathematical Society