Journal of the
Korean Mathematical Society JKMS

The present paper treats with a subfoliation of a $CR$-foliation $\mathcal F$ on an almost Hermitian manifold $M$. When $M$ is locally conformal almost K\"ahler, it has three $CR$-foliations. We show that a $CR$-foliation $\mathcal F$ on such manifold $M$ admits a canonical subfoliation ${\mathcal D}_{\mathcal F}^{\perp}$ defined by its totally real subbundle. Furthermore, we investigate some cohomology classes for ${\mathcal D}_{\mathcal F}^\perp$. Finally, we construct a new one from an old locally conformal almost K\"ahler (in particular, an almost generalized Hopf) manifold.

Keywords: locally conformal almost Kahler manifold, almost generalized Hopf manifold, $CR$-foliation, Godbillon-Vey class

MSC numbers: Primary 53C20, Secondary 57R30