Work

Critical Point Metrics of the Total Scalar Curvature

Year: 2012

Type: article

Abstract: 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.

Source: Bulletin of the Korean Mathematical Society

DOI: 10.4134/bkms.2012.49.3.655

Authors: Jeong-Wook Chang, Seung-Su Hwang, Gab-Jin Yun

Institution: Myongji University

Language: English

Topic: Geometric Analysis and Curvature Flows

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: bronze