- Current Issue - Ahead of Print Articles - All Issues - Search - Open Access - Information for Authors - Downloads - Guideline - Regulations ㆍPaper Submission ㆍPaper Reviewing ㆍPublication and Distribution - Code of Ethics - For Authors ㆍOnline Submission ㆍMy Manuscript - For Reviewers - For Editors
 Rigidity characterization of compact Ricci solitons J. Korean Math. Soc. 2019 Vol. 56, No. 6, 1475-1488 https://doi.org/10.4134/JKMS.j180747Published online November 1, 2019 Fengjiang Li, Jian Zhou East China Normal University; Yunnan Normal University Abstract : In this paper, we firstly define the Ricci mean value along the gradient vector field of the Ricci potential function and show that it is non-negative on a compact Ricci soliton. Furthermore a Ricci soliton is Einstein if and only if its Ricci mean value is vanishing. Finally, we obtain a compact Ricci soliton $(M^{n},g) (n \geq 3)$ is Einstein if its Weyl curvature tensor and the Kulkarni-Nomizu product of Ricci curvature are orthogonal. Keywords : Ricci soliton, Einstein manifold, Ricci mean value, Weyl conformal curvatue tensor MSC numbers : Primary 53C25; Secondary 53C44 Supported by : This work was financially supported by the National Natural Science Foundations of China (No.11531012 and 61663049) and Provincial Natural Science Foundation of Yunnan (No.2018FB002). Downloads: Full-text PDF   Full-text HTML