Adapted metrics on locally conformally product manifolds

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY(2024)

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Abstract
We show that the Gauduchon metric g0 of a compact locally conformally product manifold (M, c, D) of dimension greater than 2 is adapted, in the sense that the Lee form of D with respect to g0 vanishes on the D -flat distribution of M. We also characterize adapted metrics as critical points of a natural functional defined on the conformal class.
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Key words
Conformal geometry,Weyl structure,Gauduchon metric,LCP structure
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