ON LOCALLY CONFORMALLY FLAT GRADIENT SHRINKING RICCI SOLITONS

Abstract

In this paper, we first apply an integral identity on Ricci solitons to prove that closed locally conformally flat gradient Ricci solitons are of constant sectional curvature. We then generalize this integral identity to complete noncompact gradient shrinking Ricci solitons, under the conditions that the Ricci curvature is bounded from below and the Riemannian curvature tensor has at most exponential growth. As a consequence, we classify complete locally conformally flat gradient shrinking Ricci solitons with Ricci curvature bounded from below.