From Kirchberg's inequality to the Goldberg conjecture

Abstract : The main result of this note is that a compact Kaehler manifold whose Ricci tensor has two distinct constant non-negative eigenvalues is locally the product of two Kaehler-Einstein manifolds. The problem of existence of Kaehler metrics whose Ricci tensor has two distinct constant eigenvalues is related to the limiting case of Kirchberg's inequality for the first eigenvalue of the Dirac operator on compact Kaehler manifolds, as well as to the celebrated (still open) conjecture of Goldberg.
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Andrei Moroianu. From Kirchberg's inequality to the Goldberg conjecture. Dirac operators: yesterday and today, 2001, Beirut, Lebanon. pp.283-292. ⟨hal-00126086⟩

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