Total Scalar Curvature and Harmonic Curvature

Details Total Scalar Curvature and Harmonic Curvature Total Scalar Curvature and Harmonic Curvature

2011-11-29

arxiv.org/abs/1111.6861v1

Mathematics

Differential Geometry

16 pages, 2 figures

Scientific paper

On a compact n-dimensional manifold, it has been conjectured that a critical point metric of the total scalar curvature, restricted to the space of metrics with constant scalar curvature of unit volume, will be Einstein. This conjecture was proposed in 1984 by Besse, but has yet to be proved. In this paper, we prove that if the manifold with the critical point metric has harmonic curvature, then it is isometric to a standard sphere.

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