The canonical foliations of a locally conformal Kähler manifold
Three canonical foliations of a locally conformal Kähler manifold M are defined, and their properties studied. A fourth canonical foliation is defined when the Lee form of M is parallel. All of these foliations are totally geodesic and Riemannian. One of them is almost complex. If the almost complex foliation is regular, and if M is compact, it is proved that M fibers over a compact Kähler manifold with the fibers being totally geodesic flat tori. Finally the geometrical properties, the canonical class, and the Godbillon-Vey class of the totally real foliation of a CR-submanifold are studied. This paper extends the work of I. Vaisman on locally conformal Kähler manifolds and generalized Hopf manifolds.
scientific article; zbMATH DE number 3942421
scientific article