Bott-Chern formality and Massey products on strong Kähler with torsion and Kähler solvmanifolds (Q6624036)

A Hermitian metric on a complex manifold is said to be geometrically Bott-Chern formal if the wedge product of Bott-Chern harmonic forms is Bott-Chern harmonic. Recall that a Bott-Chern harmonic form is a differential form lying in the kernel of a fourth order elliptic and formally self adjoint operator called the Bott-Chern Laplacian. By Hodge theory, on a compact Hermitian manifold the space of Bott-Chern harmonic forms is isomorphic to Bott-Chern cohomology.\N\NThe authors prove that a 6-dimensional nilmanifold endowed with a left-invariant complex structure admits a SKT metric (the fundamental 2-form is pluriclosed) if and only if it admits a geometrically Bott-Chern formal metric. They also prove that every Kähler solvmanifold is geometrically Bott-Chern formal.