Some properties of curvature tensors and foliations of locally conformal almost K\"ahler manifolds

TL;DR

This paper studies properties of curvature tensors and foliations in locally conformal almost Kähler manifolds, revealing conditions under which these structures relate to almost Kähler manifolds and characterizing their canonical foliations.

Contribution

It demonstrates that under certain conditions, locally conformal almost Kähler structures form a subclass of almost Kähler structures and describes the properties of their canonical foliations.

Findings

Locally conformal almost Kähler manifolds admit a canonical foliation.

Leaves of the foliation are hypersurfaces with mean curvature proportional to the Lee vector.

Minimality of leaves correlates with the Lee vector field's incompressibility.

Abstract

We investigate a class of locally conformal almost K\"ahler structures and prove that, under some conditions, this class is a subclass of almost K\"ahler structures. We show that a locally conformal almost K\"ahler manifold admits a canonical foliation whose leaves are hypersurfaces with mean curvature vector field proportional to the Lee vector field. The geodesibility of the leaves is also characterized, and their minimality coincides with the incompressibility of the Lee vector field along the leaves.