Generalised contact geometry as reduced generalised complex geometry

TL;DR

This paper explores generalized contact structures through the lens of reduced generalized complex geometry, incorporating non-coorientable structures and describing symmetries with gerbes, leading to new generalized coKähler structures.

Contribution

It introduces a reduction framework for generalized contact structures and extends the Kähler/coKähler correspondence to this setting.

Findings

Generalized contact structures can be viewed as reductions of generalized complex structures.

Infinitesimal symmetries are characterized using gerbes.

New generalized coKähler structures are defined, extending classical geometric correspondences.

Abstract

Generalised contact structures are studied from the point of view of reduced generalised complex structures, naturally incorporating non-coorientable structures as non-trivial fibering. The infinitesimal symmetries are described in detail, with a geometric description given in terms of gerbes. As an application of the reduction procedure, generalised coK\"ahler structures are defined in a way which extends the K\"ahler/coK\"ahler correspondence.