A SPLITTING THEOREM FOR KÄHLER MANIFOLDS WHOSE RICCI TENSORS HAVE CONSTANT EIGENVALUES
A SPLITTING THEOREM FOR KÄHLER MANIFOLDS WHOSE RICCI TENSORS HAVE CONSTANT EIGENVALUES
It is proved that a compact Kahler manifold whose Ricci tensor has two distinct, constant, non-negative eigenvalues is locally the product of two Kahler-Einstein manifolds. A stronger result is established for the case of Kahler surfaces. Irreducible Kahler manifolds with two distinct, constant eigenvalues of the Ricci tensor are shown …