Hard Lefschetz Property for Isometric Flows

Abstract The hard Lefschetz property (HLP) is an important which has been studied in several categories of the symplectic world. For Sasakian manifolds, this duality satisfied by basic cohomology (so, it a transverse property), but new version HLP recently given terms manifold itself [1]. Both properties were proved to be equivalent (see [2]) case K-contact flows. In paper, we extend both versions (transverse and not) more general category isometric flows, show that they are equivalent. We also give some explicit examples illustrate where could considered.