High Quality Content by WIKIPEDIA articles! High Quality Content by WIKIPEDIA articles! In mathematics, in the field of differential geometry, the Yamabe invariant (also referred to as the sigma constant) is a real number invariant associated to a smooth manifold that is preserved under diffeomorphisms. It was first written down independently by O. Kobayashi and R. Schoen and takes its name from H. Yamabe. In the late 1990s, the Yamabe invariant was computed for large classes of 4-manifolds by LeBrun and his collaborators. In particular, it was shown that most compact complex surfaces have negative, exactly computable Yamabe invariant, and that any Kahler–Einstein metric of negative scalar curvature realizes the Yamabe invariant in dimension 4.

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