Connected sum construction of constant Q-curvature manifolds in higher dimensions

Yueh-Ju Lin

paper

Connected sum construction of constant Q-curvature manifolds in higher dimensions

arXiv:1310.0860

Abstract

For a compact Riemannian manifold $(M, g_{2})$ with constant $Q$ -curvature of dimension $n \geq 6$ satisfying nondegeneracy condition, we show that one can construct many examples of constant $Q$ -curvature manifolds by gluing construction. We provide a general procedure of gluing together $(M, g_{2})$ with any compact manifold $(N, g_{1})$ satisfying a geometric assumption. In particular, we can prove that there exists a metric with constant $Q$ -curvature on the connected sum $N #M$.