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.
Cite this article
Takayuki Moriyama, Deformations of Transverse Calabi–Yau Structures on Foliated Manifolds. Publ. Res. Inst. Math. Sci. 46 (2010), no. 2, pp. 335–357DOI 10.2977/PRIMS/11