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arXiv · 2103.15482

Besse conjecture with positive isotropic curvature

Seungsu Hwang·Gabjin Yun
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Abstract

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 $$ (1+f){\rm Ric} = Ddf + \frac{nf +n-1}{n(n-1)}sg. $$ 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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Seungsu Hwang, Gabjin Yun. 2021-03-29. Besse conjecture with positive isotropic curvature. https://arxiv.org/abs/2103.15482

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