Multiplicity of constant scalar curvature metrics in Tk×MTk×M

We use bifurcation theory to prove the existence of uncountably many unit volume constant scalar curvature metrics in manifolds of the form Tk×MTk×M, k≥2k≥2, with MM a compact manifold (without boundary), that are conformal, but not isometric, to a product metric gflat⊕g, where gflat is a flat metric on the kk-torus TkTk, and gg is a fixed constant scalar curvature metric on MM.