秩为2的五维K-切触流形
Five dimensional K-contact manifolds of rank 2
摘要：
K-切触流形是具有切触形式的光滑流形M，其Reeb流保持M上的黎曼度量。主要的例子是Sasakian流形。本文的结果是将莫尔斯理论应用于秩为2的闭5维K-切触流形上的切触矩映射得到的以下四个结果i），ii），iii）和iv）. 5-秩为2的维K-切触流形在具有非环面的非平凡接触矩映射的K-切触流形中具有最低的维数。i）K-切触流形的同构类与各向同性数据的图之间的对应，ii）K-切触流形的分类直到接触的上下爆破，iii）每个秩为2的闭5维K-切触流形都有Sasaki度量，iv）秩为2的闭5维K-切触流形是切触环面的一个充分条件.
英文摘要：
A K-contact manifold is a smooth manifold M with a contact form whose Reeb flow preserves a Riemannian metric on M. Main examples are Sasakian manifolds. Our results in this paper are four results i), ii), iii) and iv) below obtained by the application of the Morse theory to the contact moment maps on closed 5-dimensional K-contact manifolds of rank 2. 5-dimensional K-contact manifolds of rank 2 have the lowest dimension among K-contact manifolds with nontrivial contact moment maps which are not toric. i) Correspondence between the isomorphism classes of K-contact manifolds and graphs of isotropy data, ii) Classification of K-contact manifolds up to contact blowing up and down, iii) Every closed 5-dimensional K-contact manifold of rank 2 has a Sasakian metric, iv) A sufficient condition for closed 5-dimensional K-contact manifolds of rank 2 to be contact toric.
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