CRITICAL POINT METRICS OF THE TOTAL SCALAR CURVATURE

Jeong-Wook Chang, Seung-Su Hwang, Gab-Jin Yun
2012 Bulletin of the Korean Mathematical Society  
In this paper, we deal with a critical point metric of the total scalar curvature on a compact manifold 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 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.
doi:10.4134/bkms.2012.49.3.655 fatcat:gfvbsfxnqvfj7n5pttk7ge2xsi