论文标题
弱形式平坦和准爱因斯坦歧管的表征
Characterizations Of Weakly Conformally Flat And Quasi Einstein Manifolds
论文作者
论文摘要
首先，我们表明一条线和纤维歧管的扭曲产物在且仅当纤维是爱因斯坦时，是弱的保态和准爱因斯坦。接下来，我们对触点（尤其是$ k $ - 连接）进行了表征和分类，riemannian歧管很弱（且双重弱）扁平（双重弱）和Quasi-Einstein（$η$ -Einstein）条件。最后，我们在Petrov类型和BACH张量方面提供了具有谐波Weyl张量和非所有人的共形的局部分类和表征，并具有谐波Weyl张量和非所有人的共形（包括封闭式）矢量场的局部分类和表征。
First, we show that a warped product of a line and a fiber manifold is weakly conformally flat and quasi Einstein if and only if the fiber is Einstein. Next, we characterize and classify contact (in particular, $K$-contact) Riemannian manifold satisfying weakly (and doubly weakly) conformally flat and quasi-Einstein ($η$-Einstein) conditions. Finally, we provide local classification and characterization of a semi-Riemannian (including the 4-dimensional spacetime) with harmonic Weyl tensor and a non-homothetic conformal (including closed) vector field, in terms of Petrov types and Bach tensor.
