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 . 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 -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;
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