标题： 几乎准Sasakian流形配备反对称连接 显示英文标题

标题： Almost quasi-Sasakian manifolds equipped with skew-symmetric connection

摘要： 在子黎曼流形上，一个具有反对称挠率的联络被定义为从$N$类联络中唯一具有该性质的联络。 分别考虑两种情况：偶数秩的子黎曼结构，以及奇数秩的子黎曼结构。 当子黎曼结构为偶数秩时，所得的联络称为规范联络，此时它不是度量联络。 几乎准Sasakian流形的结构被定义为满足额外条件的奇数秩几乎接触度量结构。 具体来说，要求规范联络是度量联络，并且横截结构是Kähler结构。 几乎Sasakian结构和更一般的几乎接触度量结构，称为几乎准Sasakian结构，都满足这些条件。 找到了使几乎准Sasakian流形成为爱因斯坦流形的充分条件。 显示英文摘要

摘要： On a sub-Riemannian manifold, a connection with skew-symmetric torsion is defined as the unique connection from the class of $N$-connections that has this property. Two cases are considered separately: sub-Riemannian structure of even rank, and sub-Riemannian structure of odd rank. The resulting connection, called the canonical connection, is not a metric connection in the case when the sub-Riemannian structure is of even rank. The structure of an almost quasi-Sasakian manifold is defined as an almost contact metric structure of odd rank that satisfies additional requirements. Namely, it is required that the canonical connection is a metric connection and that the transversal structure is a K\"ahler structure. Both the quasi-Sasakian structure and the more general almost contact metric structure, called an almost quasi-Sasakian structure, satisfy these requirements. Sufficient conditions are found for an almost quasi-Sasakian manifold to be an Einstein manifold.