Besse conjecture with positive isotropic curvature

초록

The critical point equation arises as a critical point of the total scalar curvature functional defined on the space of constant scalar curvature metrics of a unit volume on a compact manifold. In this equation, there exists a function f on the manifold that satisfies the following (1 + f)Ric = Ddf + nf + n - 1/n(n - 1)sg. It has been conjectured that if (g, f) is a solution of the critical point equation, then g is Einstein and so (M, g) is isometric to a standard sphere. In this paper, we show that this conjecture is true if the given Riemannian metric has positive isotropic curvature.

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