Local Structure of Vaisman–Gray Manifolds

Abstract

In this paper, we introduce the notion of a mapping of adjoint G-structures of almost Hermitian manifolds and obtain relations between components of the fundamental tensor fields of an initial almost Hermitian manifold and the conformally transformed manifold. These formulas are applied to the study of the class of Vaisman–Gray manifolds. We prove that in dimension > 4 the class of Vaisman–Gray manifolds coincides with the class of locally conformally nearly K¨ahlerian manifolds.