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A β-tensor on Kaehler manifolds and its geometric characterizations
International Journal of Geometric Methods in Modern Physics ( IF 2.1 ) Pub Date : 2021-07-07 , DOI: 10.1142/s0219887821501838
Şemsi Eken Meriç 1
Affiliation  

In this paper, we first introduce a new notion β-tensor on Hermitian manifold and particularly, we present some geometric characterizations of such a tensor on the Kaehler manifold. Here, we investigate the Kaehler submersion whose total space is equipped with the β-tensor and obtain some results. Also, we deal with a Kaehler submersion with totally geodesic fibers such that the total space admits -Ricci soliton and β-tensor. Finally, we give necessary conditions for which any fiber and base manifold of Kaehler submersion is -Ricci soliton or -Kaehler-Einstein.

中文翻译:

Kaehler 流形上的一个 β-张量及其几何表征

在本文中,我们首先介绍一个新概念β-Hermitian 流形上的张量,特别是,我们提出了 Kaehler 流形上这种张量的一些几何特征。在这里,我们研究了总空间配备有β-张量并获得一些结果。此外,我们使用完全测地线纤维处理 Kaehler 浸没,使得总空间允许*-里奇孤子和β-张量。最后,我们给出了凯勒浸没的任何纤维和基流形的必要条件*-里奇孤子或*——凯勒-爱因斯坦。
更新日期:2021-07-07
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