The basic $dd^{\mathcal{J}}$-lemma
Differential Geometry
2017-01-09 v7
Abstract
The purpose of this short paper is to further develop the theory of transverse generalized complex structures. We focus on proving some equivalent conditions to the basic -lemma. We justify our approach by describing the transverse symplectic structure in this language and relating the basic -lemma to the surjectivity of the Lefschetz map. We also present a non-trivial example of a foliation endowed with a transverse generalized complex structure. Transverse generalized complex structures do not rely heavily on the existence of a bundle-like metric, which makes them a convienient tool to study some non-Riemmanian foliations.
Cite
@article{arxiv.1609.04539,
title = {The basic $dd^{\mathcal{J}}$-lemma},
author = {Pawel Razny},
journal= {arXiv preprint arXiv:1609.04539},
year = {2017}
}