This is an exposition of the subject, which was developed in the author’s papers [19, 20]. Various results from the theory of foliations (cohomology, characteristic classes, deformations, etc.) are… Expand

Double field theory was developed by theoretical physicists as a way to encompass T -duality. In this paper, we express the basic notions of the theory in differential-geometric invariant terms, in… Expand

In a previous paper, we have shown that the geometry of double field theory has a natural interpretation on flat para-Kahler manifolds. In this paper, we show that the same geometric constructions… Expand

Double field theory was developed by theoretical physicists as a way to encompass T-duality. In this paper, we express the basic notions of the theory in differential-geometric invariant terms in the… Expand

In his study of Dirac structures, a notion which includes both Poisson structures and closed 2-forms, T. Courant introduced a bracket on the direct sum of vector fields and 1-forms. This bracket does… Expand

If A is a Lie algebroid over a foliated manifold $${(M, {\mathcal {F}})}$$, a foliation of A is a Lie subalgebroid B with anchor image $${T{\mathcal {F}}}$$ and such that A/B is locally equivalent… Expand