Publications of the Research Institute for Mathematical Sciences

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Volume 46, Issue 2, 2010, pp. 335–357
DOI: 10.2977/PRIMS/11

Published online: 2010-06-07

Deformations of Transverse Calabi–Yau Structures on Foliated Manifolds

Takayuki Moriyama[1]

(1) Kyoto University, Japan

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.

Keywords: Foliation, transverse Calabi–Yau structure, deformation theory

Moriyama Takayuki: Deformations of Transverse Calabi–Yau Structures on Foliated Manifolds. Publ. Res. Inst. Math. Sci. 46 (2010), 335-357. doi: 10.2977/PRIMS/11