Thek-Yamabe solitons and the quotient Yamabe solitons

In this paper, we consider the solitons to the fully nonlinear type Yamabe flows. We prove that any k -Yamabe soliton with positive k -curvature must have constant σ k -curvature on closed locally conformally flat manifolds. We also prove that any quotient Yamabe soliton with positive k and l curvatures must have constant σ k σ l -curvature on closed locally conformally flat manifolds. Similar results are also proved on compact locally conformally flat manifolds with totally geodesic boundary.