Hard Lefschetz Property for Isometric Flows

TL;DR

This paper extends the Hard Lefschetz Property to isometric flows, demonstrating their equivalence and providing explicit examples, thereby broadening understanding of duality properties in geometric structures.

Contribution

It introduces a generalized version of the Hard Lefschetz Property for isometric flows and proves their equivalence, expanding the scope beyond Sasakian and K-contact manifolds.

Findings

HLP extended to isometric flows

Equivalence of transverse and non-transverse HLP established

Explicit examples illustrating applicable categories

Abstract

The Hard Lefschetz Property (HLP) is an important property which has been studied in several categories of the symplectic world. For Sasakian manifolds, this duality is satisfied by the basic cohomology (so, it is a transverse property), but a new version of the HLP has been recently given in terms of duality of the cohomology of the manifold itself in arXiv:1306.2896. Both properties were proved to be equivalent (see arXiv:1311.1431) in the case of K-contact flows. In this paper we extend both versions of the HLP (transverse and not) to the more general category of isometric flows, and show that they are equivalent. We also give some explicit examples which illustrate the categories where the HLP could be considered.