arXiv 1609.045392016-09math.DG

The basic $dd^{\mathcal{J}}$-lemma

Pawel Razny

英文摘要：

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 $dd^{\mathcal{J}}$ -lemma. We justify our approach by describing the transverse symplectic structure in this language and relating the basic $dd^{\mathcal{J}}$-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.

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