Abstract:
It is well known that critical points of the total scalar curvature functional ? on the space of all smooth Riemannian structures of volume 1 on a compact manifold M are exactly the Einstein metrics. When the domain of ? is restricted to the space of constant scalar curvature metrics, there has been a conjecture that a critical point is also Einstein or isometric to a standard sphere. In this paper we prove that n-dimensional critical points have vanishing n− 1 homology under a lower Ricci curvature bound for dimension less than 8.
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Received: 12 July 1999
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Hwang, S. Critical points of the total scalar curvature functional on the space of metrics of constant scalar curvature. manuscripta math. 103, 135–142 (2000). https://doi.org/10.1007/PL00005857
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DOI: https://doi.org/10.1007/PL00005857