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Hitchin sections on $3$-dimensional Sasakian manifolds
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 SL2(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.
Related
- Three-dimensional noncompact trans-Sasakian η-Einstein manifolds
- Cusp cross-sections of low-dimensional arithmetic hyperbolic manifolds
- Laplace and Dolbeault operators on Sasakian manifolds
- Characterization of Sasakian Manifolds by Curvature Conditions
- Partially Totally Real Submanifolds of Sasakian Manifolds
BibTeX
@misc{kasuya2026hitchin,
title = {{Hitchin sections on $3$-dimensional Sasakian manifolds}},
author = {Hisashi Kasuya},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.06919},
eprint = {2609.06919},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.06919},
}
RIS
TY - UNPB
TI - Hitchin sections on $3$-dimensional Sasakian manifolds
AU - Hisashi Kasuya
PY - 2026
DA - 2026/09/07
PB - arXiv
DO - 10.48550/arxiv.2609.06919
UR - https://arxiv.org/abs/2609.06919
AB - 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 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.
ER -