Symplectic structures on low dimensional 2-step nilmanifolds

TL;DR

This paper investigates symplectic structures on low-dimensional 2-step nilmanifolds, establishing conditions under which closed 2-forms lead to symplectic structures, with most cases in low dimensions satisfying these conditions.

Contribution

It identifies the necessity of closed 2-forms of type II for symplectic structures and shows that this condition is sufficient in most low-dimensional cases.

Findings

Existence of closed 2-forms of type II is necessary for symplectic structures.

In low dimensions, this condition is sufficient for most cases.

Provides criteria for symplectic structures on 2-step nilmanifolds.

Abstract

The aim of this work is the study of symplectic structures on 2-step nilmanifolds. We concentrate in the closeness condition, proving that the existence of a closed 2-form of type II is necessary to get a symplectic structure. In low dimensions, this condition is sufficient in most cases.