2011年6月

# THE MODULI SPACE OF TRANSVERSE CALABI-YAU STRUCTURES ON FOLIATED MANIFOLDS

OSAKA JOURNAL OF MATHEMATICS
• Takayuki Moriyama

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OSAKA JOURNAL OF MATHEMATICS

In this paper, we develop a moduli theory of transverse structures given by calibrations on foliated manifolds, including transverse Calabi-Yau structures. We show that the moduli space of the transverse structures is a smooth manifold of finite dimension under a cohomological assumption. We also prove a local Torelli type theorem. If the foliation is taut, we can construct a Riemannian metric on the set of transverse Riemannian structures. This metric induces a distance on the moduli space of the transverse structures given by a calibration. As an application, we show the moduli space of transverse Calabi-Yau structures is a Hausdorff and smooth manifold of finite dimension.

Web of Science ® 被引用回数 : 3

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