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http://dx.doi.org/10.4134/JKMS.j180747

RIGIDITY CHARACTERIZATION OF COMPACT RICCI SOLITONS

Li, Fengjiang (Department of Mathematics East China Normal University)
Zhou, Jian (Department of Mathematics Yunnan Normal University)

Publication Information

Journal of the Korean Mathematical Society / v.56, no.6, 2019 , pp. 1475-1488 More about this Journal

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;

Citations & Related Records

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