Hitchin截面在三维Sasakian流形上
Hitchin sections on $3$-dimensional Sasakian manifolds
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- Graduate School of Mathematics, Nagoya University（名古屋大学大学院数学研究科）
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中文总结 AI 辅助
利用非阿贝尔Hodge对应，在三维紧致Sasakian流形上构造秩2的Hitchin截面，通过典范形变建立基本二次微分空间与特定Sasakian结构等价类空间的微分同胚。
中文摘要 AI 辅助
通过利用紧致Sasakian流形上的非阿贝尔Hodge对应，我们研究了秩$2$的Hitchin截面在三维紧致Sasakian流形上的类似构造。我们获得了$\widetilde{SL_{2}(\R)}$-Sasakian结构的典范形变，该形变给出了从基本二次微分向量空间到具有负基本第一Chern类和拓扑平凡CR结构（配备适当流形结构）的Sasakian结构等价类空间的连通分量的微分同胚。
英文摘要
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.
