论文标题
$η$ - 正常，CR结构，几乎接触度量的Para-CR结构和几乎Paracontact Mardric歧管
$η$-Normality, CR-structures, para-CR structures on almost contact metric and almost paracontact metric manifolds
论文作者
论文摘要
对于几乎接触度量或几乎是Paracontact公制歧管，有$η$ normality的自然概念。如果沿特征形式的内核分布是正常的，则歧管称为$η$ - 正常。在本文中，证明$η$ - 正常的歧管在几乎是副触发式歧管的情况下，与Cauchy-Riemann几乎接触度量歧管或Para Cauchy-Riemann是一对一的信件。根据结构张量的Levi-Civita协变量衍生物，提供了$η$ - 正常的歧管的表征。它建立在$η$ - 正常的歧管上，具有自动Parallear Reeb vector Field的存在。特别是与公制CR-Manifold联系，这是通常的田中连接。几乎可以为几乎Paracontact公制歧管获得类似的结果。对于具有封闭基本形式的歧管，我们将说明这种联系的独特性。在最后一部分中，研究了几乎具有接触特征形式的几乎副触发型歧管的双层结构。已经确定，这种歧管是双legendrian平坦的，并且仅在正常时才。有特征性的半光定双灯 - 莱根式歧管。
For almost contact metric or almost paracontact metric manifolds there is natural notion of $η$-normality. Manifold is called $η$-normal if is normal along kernel distribution of characteristic form. In the paper it is proved that $η$-normal manifolds are in one-one correspondence with Cauchy-Riemann almost contact metric manifolds or para Cauchy-Riemann in case of almost paracontact metric manifolds. There is provided characterization of $η$-normal manifolds in terms of Levi-Civita covariant derivative of structure tensor. It is established existence a Tanaka-like connection on $η$-normal manifold with autoparallel Reeb vector field. In particular case contact metric CR-manifold it is usual Tanaka connection. Similar results are obtained for almost paracontact metric manifolds. For manifold with closed fundamental form we shall state uniqueness of this connection. In the last part is studied bi-Legendrian structure of almost paracontact metric manifold with contact characteristic form. It is established that such manifold is bi-Legendrian flat if and only if is normal. There are characterized semi-flat bi-Legendrian manifolds.
