Hitchin sections on $3$-dimensional Sasakian manifolds

Hisashi Kasuya

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arXiv · 2609.06919

Hitchin sections on $3$-dimensional Sasakian manifolds

Hisashi Kasuya

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Abstract

By using non-abelian Hodge correspondence on compact Sasakian manifolds, we investigate analogous constructions of Hitchin sections of rank $2$ on $3$-dimensional compact Sasakian manifolds. We obtain canonical deformations of $\widetilde{SL_{2}(\R)}$-Sasakian structures giving a diffeomorphism from the vector space of basic quadratic differentials onto a connected component of the space of equivalent classes of sasakian structures of negative basic first Chern classes and topologically trivial CR structures equipped with an appropriate manifold structure.

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BibTeX RIS

Hisashi Kasuya. 2026-09-07. Hitchin sections on $3$-dimensional Sasakian manifolds. https://arxiv.org/abs/2609.06919

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