The Ricci-flat projective-induction conjecture

A Ricci-flat metric is a Kähler metric whose Ricci curvature vanishes, and a metric is projectively induced if it admits a Kähler immersion into some projective space $\mathbb{C}P^N$ or $\mathbb{C}P^{\infty}$. The Ricci-flat projective-induction conjecture. Every Ricci-flat projectively induced metric is flat. The conjecture is motivated by the nonexistence of projective Kähler immersions for compact Calabi–Yau manifolds and by nonflat Ricci-flat examples such as the Taub–NUT metrics, which are not projectively induced in the stated range of parameters. Its general status is not resolved in the source.