CRITICAL POINT METRICS OF THE TOTAL SCALAR CURVATURE

Title & Authors
CRITICAL POINT METRICS OF THE TOTAL SCALAR CURVATURE
Chang, Jeong-Wook; Hwang, Seung-Su; Yun, Gab-Jin;

Abstract
In this paper, we deal with a critical point metric of the total scalar curvature on a compact manifold $\small{M}$. We prove that if the critical point metric has parallel Ricci tensor, then the manifold is isometric to a standard sphere. Moreover, we show that if an $\small{n}$-dimensional Riemannian manifold is a warped product, or has harmonic curvature with non-parallel Ricci tensor, then it cannot be a critical point metric.
Keywords
the total scalar curvature;critical point metric;Einstein;
Language
English
Cited by
1.
THREE DIMENSIONAL CRITICAL POINT OF THE TOTAL SCALAR CURVATURE,;

대한수학회보, 2013. vol.50. 3, pp.867-871
1.
A note on critical point metrics of the total scalar curvature functional, Journal of Mathematical Analysis and Applications, 2015, 424, 2, 1544
2.
THREE DIMENSIONAL CRITICAL POINT OF THE TOTAL SCALAR CURVATURE, Bulletin of the Korean Mathematical Society, 2013, 50, 3, 867
3.
Critical metrics of the total scalar curvature functional on 4-manifolds, Mathematische Nachrichten, 2015, 288, 16, 1814
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