Tohoku Mathematical Journal
2021
March
SECOND SERIES VOL. 73, NO. 1

Tohoku Math. J.
73 (2021), 29-37

Title RICCI FLAT CALABI'S METRIC IS NOT PROJECTIVELY INDUCED

Author Andrea Loi, Michela Zedda and Fabio Zuddas

(Received August 16, 2019)
Abstract. We show that the Ricci flat Calabi's metrics on holomorphic line bundles over compact Kähler--Einstein manifolds are not projectively induced. As a byproduct we solve a conjecture addressed in [10] by proving that any multiple of the Eguchi-Hanson metric on the blow-up of $\mathds{C}^2$ at the origin is not projectively induced.

Mathematics Subject Classification. Primary 53C55; Secondary 58C25, 58F06.
Key words and phrases. Calabi's diastasis function, Ricci flat metric, projectively induced metric, flag manifold.

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