Ricci flat Calabi's metric is not projectively induced

TL;DR

This paper proves that Ricci flat Calabi's metrics on certain complex manifolds and multiples of the Eguchi-Hanson metric are not projectively induced, resolving a specific conjecture in complex differential geometry.

Contribution

It demonstrates that these Ricci flat metrics and multiples of the Eguchi-Hanson metric cannot be realized as projectively induced, providing new insights into their geometric properties.

Findings

Ricci flat Calabi's metrics are not projectively induced

Multiples of the Eguchi-Hanson metric are not projectively induced

Resolved a conjecture regarding the Eguchi-Hanson metric

Abstract

We show that the Ricci flat Calabi's metrics on holomorphic line bundles over compact Kaehler-Einstein manifolds are not projectively induced. As a byproduct we solve a conjecture addressed in [arXiv:1705.03908v2 [math.DG]] by proving that any multiple of the Eguchi-Hanson metric on the blow-up of C^2 at the origin is not projectively induced.