Although Ricci curvature is defined for any Riemannian manifold, it plays a special role in Kähler geometry: the Ricci curvature of a Kähler manifold "X" can be viewed as a real closed (1,1)-form that represents "c"1("X") (the first Chern class of the tangent bundle) in . It follows that a compact Kähler–Einstein manifold "X" must have canonical bundle "K""X" either anti-ample, homologically trivial, or ample, depending on whether the Einstein constant λ is positive, zero, or negative. Kähler manifolds of those three types are called Fano, Calabi–Yau, or with ample canonical bundle (which implies general type), respectively. By the Kodaira embedding theorem, Fano manifolds and manifolds with ample canonical bundle are automatically projective varieties.