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June 2011 The moduli space of transverse Calabi--Yau structures on foliated manifolds
Takayuki Moriyama
Osaka J. Math. 48(2): 383-413 (June 2011).

Abstract

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.

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Takayuki Moriyama. "The moduli space of transverse Calabi--Yau structures on foliated manifolds." Osaka J. Math. 48 (2) 383 - 413, June 2011.

Information

Published: June 2011
First available in Project Euclid: 6 September 2011

zbMATH: 1247.53030
MathSciNet: MR2831979

Subjects:
Primary: 53C12
Secondary: 35C38

Rights: Copyright © 2011 Osaka University and Osaka City University, Departments of Mathematics

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Vol.48 • No. 2 • June 2011
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