On Weyl tensor of ACR-manifolds of class $C_{12}$ with applications

IF 0.3 Q4 MATHEMATICS
A. Mohammed Yousif, Qusay S. A. Al-Zamil
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引用次数: 0

Abstract

In this paper, we determine the components of the Weyl tensor of almost contact metric (ACR-) manifold of class $C_{12}$ on associated G-structure (AG-structure) space. As an application, we prove that the conformally flat ACR-manifold of class $C_{12}$ with $n>2$ is an $\eta$-Einstein manifold and conclude that it is an Einstein manifold such that the scalar curvature $r$ has provided. Also, the case when $n=2$ is discussed explicitly. Moreover, the relationships among conformally flat, conformally symmetric, $\xi$-conformally flat and $\Phi$-invariant Ricci tensor have been widely considered here and consequently we determine the value of scalar curvature $r$ explicitly with other applications. Finally, we define new classes with identities analogously to Gray identities and discuss their connections with class $C_{12}$ of ACR-manifold.
类$C_{12}$ acr流形的Weyl张量及其应用
本文确定了相关g结构(ag -结构)空间上$C_{12}$类几乎接触度量流形(ACR-)的Weyl张量的分量。作为应用,我们证明了含有$n>2$类$C_{12}$的共形平坦acr流形是$\eta$ -爱因斯坦流形,并得出它是标量曲率$r$所提供的爱因斯坦流形。此外,还明确地讨论了$n=2$的情况。此外,本文还广泛地考虑了共形平坦、共形对称、$\xi$ -共形平坦和$\Phi$ -不变Ricci张量之间的关系,从而通过其他应用明确地确定了标量曲率$r$的值。最后,我们定义了类似于Gray恒等式的新类,并讨论了它们与acr流形中$C_{12}$类的联系。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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