On Calabi extremal Kaehler-Ricci solitons

Abstract

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.

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References in corpus (2)

• Canonical Sasakian Metrics
• Existence of Gradient Kahler-Ricci Solitons

Cited by in corpus (1)

• Toric extremal Kaehler-Ricci solitons are Kaehler-Einstein