Invariant contact structures on 7-dimensional nilmanifolds

TL;DR

This paper classifies all 7-dimensional nilpotent Lie algebras and nilmanifolds that support invariant contact structures, providing a comprehensive list and description of such geometric structures.

Contribution

It provides the first complete classification of 7-dimensional nilpotent Lie algebras and nilmanifolds admitting invariant contact structures.

Findings

List of all 7-dimensional nilpotent Lie algebras with contact structures

Description of all 7-dimensional nilmanifolds with invariant contact structures

Complete classification results for these geometric structures

Abstract

In this paper we give the list of all 7-dimensional nilpotent real Lie algebras that admit a contact structure. Based on this list, we describe all 7-dimensional nilmanifolds that admit an invariant contact structure.