Conformally recurrent pseudo-Riemannian manifolds of dimension n>4 are investigated. The Weyl tensor is represented as a Kulkarni-Nomizu product. If the square of the Weyl tensor is nonzero, a covariantly constant symmetric tensor is constructed, that is quadratic in the Weyl tensor. Then, by Grycak's theorem, the explicit expression of the traceless part of the Ricci tensor is obtained, up to a scalar function. The Ricci tensor has at most two distinct eigenvalues, and the recurrence vector is an eigenvector. Lorentzian conformally recurrent manifolds are then considered. If the square of the Weyl tensor is nonzero, the manifold is decomposable. A null recurrence vector makes the Weyl tensor of algebraic type IId or higher in the Bel - Debever - Ortaggio classification, while a time-like recurrence vector makes the Weyl tensor purely electric.
Conformally invariant Cotton and Bach tensor in N-dimensions
本文给出了维数大于或等于4的黎曼流形的共形不变量，其消元是黎曼流形与Einstein空间共形相关的必要条件.其中一个不变量是科顿张量的修改，另一个是巴赫张量的$n$维版本。一般来说，这两个张量只在$M$的一个开的稠密子集上是光滑的，但这个子集在保形变换下是不变的。进一步推广了发表在\emph{Ann. Global Anal. Geom.} { \bf 20}（2）（2001）中的“Conformal Einstein Spaces in $N$ --Dimensions”的主要结果.
On the existence of a generalized class of recurrent manifolds
本文研究了一类广义回归流形，即超广义回归流形的真存在性。我们已经建立了递归流形的各种广义概念的正确存在性。为此，我们提出了一个度量，并计算了它的曲率性质，最后得到了一类新的半黎曼流形的存在性，它们是非递归的，但却是超广义递归的、Ricci递归的、共调和递归的、具有递归曲率2-形式的流形和半对称的;非爱因斯坦但Ricci简单;不满足$P\cdot P =0$但满足条件$P \cdot P = -\frac{1}{3}Q(S, P)$，$P$是投影曲率张量。
