A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2017; you can also visit the original URL.
The file type is
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