论文标题
简单连接的5个manifolds上的负Sasakian结构
Negative Sasakian structures on simply-connected 5-manifolds
论文作者
论文摘要
我们研究了几个关于简单连接的有理同源性领域以及形式$ \ #_ k（s^2 \ times s^3）$的萨萨基亚结构的存在的问题。首先，我们证明，任何简单地连接的理性同源性领域都承认萨萨基人的结构也承认了负面的结构。这个结果回答了Boyer和Galicki在他们的书[BG]中提出的问题，确定哪个简单地联系在一起的合理同源性领域既承认负面和积极的Sasakian结构。其次，我们证明了连接的总和$ \ #_ k（s^2 \ times s^3）$允许对任何$ k $的负质量sasakian结构负。这对[BG]中提出的另一个问题产生了完整的答案。
We study several questions on the existence of negative Sasakian structures on simply connected rational homology spheres and on Smale-Barden manifolds of the form $\#_k(S^2\times S^3)$. First, we prove that any simply connected rational homology sphere admitting positive Sasakian structures also admits a negative one. This result answers the question, posed by Boyer and Galicki in their book [BG], of determining which simply connected rational homology spheres admit both negative and positive Sasakian structures. Second, we prove that the connected sum $\#_k(S^2\times S^3)$ admits negative quasi-regular Sasakian structures for any $k$. This yields a complete answer to another question posed in [BG].
