TOTAL SCALAR CURVATURE AND HARMONIC CURVATURE
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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.
16 pages, 2 figures
- Chung-Ang University Korea (Republic of)
- Dankook University Korea (Republic of)
Mathematics - Differential Geometry, 53c25, 58e11, total scalar curvature, Differential Geometry (math.DG), harmonic curvature, FOS: Mathematics, Einstein metric, 58E11, critical point metric, 53C25
Mathematics - Differential Geometry, 53c25, 58e11, total scalar curvature, Differential Geometry (math.DG), harmonic curvature, FOS: Mathematics, Einstein metric, 58E11, critical point metric, 53C25
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