Deformations of Transverse Calabi–Yau Structures on Foliated Manifolds

Abstract

We develop a deformation theory of transverse structures given by calibrations on foliated manifolds, including transverse Calabi–Yau, hyperkähler, G2 and Spin(7) structures. We a show that the deformation space of the transverse structures is smooth under a cohomological assumption. As an application, we obtain unobstructed deformations of transverse Calabi–Yau structures on foliated manifolds. We also prove a Moser type stability result for transverse structures, which implies Moser’s stability theorem for presymplectic forms.