Adapted metrics on locally conformally product manifolds

Abstract

We show that the Gauduchon metric g 0 g_0 of a compact locally conformally product manifold ( M , c , D ) (M,c,D) of dimension greater than 2 2 is adapted, in the sense that the Lee form of D D with respect to g 0 g_0 vanishes on the D D -flat distribution of M M . We also characterize adapted metrics as critical points of a natural functional defined on the conformal class.