On some rigidity theorems of Q-curvature

In this paper, we investigate the rigidity of Q-curvature. Specifically, we consider a closed, oriented n -dimensional ( n ≥ 6 ) Riemannian manifold ( M , g ) and prove the following results under the condition . (1) If ( M , g ) is locally conformally flat with nonnegative Ricci curvature, then ( M , g ) is isometric to a quotient of R n , S n , or R × S n - 1 . (2) If ( M , g ) has δ 2 W = 0 with nonnegative sectional curvature, then ( M , g ) is isometric to a quotient of the product of Einstein manifolds. Additionally, we investigate some rigidity theorems involving Q-curvature about hypersurfaces in simply-connected space forms. We also show the uniqueness of metrics with constant scalar curvature and constant Q-curvature in a fixed conformal class.