Calabi-Yau Foliations and Deformations

2024/12/10 by Rémi Danain-Bertoncini, Danain-Bertoncini, Rémi
Mathematics · Engineering · #Geometric Analysis and Curvature Flows #Seismic Performance and Analysis #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2412.07566

Abstract

We propose in this article the study of the deformations of a Calabi-Yau type foliations F. For three different types of deformations (unfoldings, holomorphic, transversally holomorphic) there exist Kuranishi spaces K^f,K^h,K^tr parametrizing the corresponding families of deformations. We show that K^f is smooth, and that we can obtain K^h as the product K^f× K^tr. At last, we show that we can see the f-deformations of F as the tr-deformations of a supplementary foliation G.

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