Two rigidity theorems for fully nonlinear equations

This paper is concerned with the fully nonlinear equation σ2(g)=aσ1(g)+b. The first result is to obtain the entire solutions of the equation for conformally flat metric on Rn under some additional assumptions, which generalizes the famous result of Chang-Gursky-Yang in [3]. The second one is to classify compact locally conformally flat manifolds with nonnegative Ricci curvature and the metric g satisfying the equation.