A class of locally conformal almost cosymplectic manifolds
In this paper, the authors consider a class of almost contact metric manifolds called locally conformal almost cosymplectic manifolds. They prove several results linking the parallelism of the Chern-Hamilton tensor and the property of the characteristic vector field to be Killing. This last condition \(({\mathcal{L}}_\xi g=0)\) implies that the manifold is almost cosymplectic. Then, the authors are interested in the case when the closed 1-form \(\omega\) (appearing in the locally conformal structure) and the 1-form \(\eta\) are proportional. Later on, they consider a foliation on a locally conformal almost cosymplectic manifold of codimension 1 and study when the metric is bundle-like for the foliation. Under some conditions, the foliation of the contact distribution has (almost) Kählerian leaves. Some examples are given.
scientific article; zbMATH DE number 6864642
scientific article