Locally conformal SKT structures

A Hermitian metric on a complex manifold is called SKT (strong Kähler with torsion) if the Bismut torsion 3-form [Formula: see text] closed. As conformal generalization of condition, we introduce new type structure, locally (or shortly LCSKT). More precisely, structure said to be LCSKT there exists closed nonzero text]-form such that text]. In this paper, consider nontrivial structures, i.e. assume and study their existence Lie groups compact quotients by lattices. particular, classify six-dimensional nilpotent algebras admitting show that, in contrast case, 3-step algebra structure. Moreover, characterization even dimensional almost abelian which allows us construct explicit examples unimodular The compatibility between balanced condition also discussed, showing or text]-dimensional cannot simultaneously balanced, unless it Kähler.