Deformations of Transverse Calabi–Yau Structures on Foliated Manifolds | Zendy

Takayuki Moriyama | Zendy

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Deformations of Transverse Calabi–Yau Structures on Foliated Manifolds

Author(s) -

Takayuki Moriyama

Publication year - 2010

Publication title -

publications of the research institute for mathematical sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.786

H-Index - 39

eISSN - 1663-4926

pISSN - 0034-5318

DOI - 10.2977/prims/11

Subject(s) - transverse plane , mathematics , deformation (meteorology) , holonomy , calabi–yau manifold , space (punctuation) , hyperkähler manifold , stability (learning theory) , pure mathematics , geometry , ricci flat manifold , physics , structural engineering , computer science , engineering , scalar curvature , curvature , machine learning , meteorology , operating system

We develop a deformation theory of transverse structures given by calibrations on foliated manifolds, including transverse Calabi{Yau, hyperkahler, G2 and Spin(7) structures. We show that the deformation space of the transverse structures is smooth under a cohomo- logical 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.

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