Abstract

The purpose of the present paper is to study Ricci solitons on Sasaki–Kenmotsu manifolds. It is shown that if the characteristic vector fields \(\xi\) and \(\psi\) are recurrent torse-forming vector fields on the Sasaki–Kenmotsu metric as a Ricci soliton, then both \(\xi\) and \(\psi\) are concurrent and Killing vector fields. We classify and characterize a Sasaki–Kenmotsu manifold admitting holomorphically planar conformal vector \((HPCV)\) field. Also, we prove that an \(HPCV\) field on a Sasaki–Kenmotsu manifold is solenoidal. Moreover, in a Sasaki–Kenmotsu manifold admitting \(HPCV\) field \(V\) with \(\phi V\neq 0\), the \(HPCV\) field is the eigen vector of the Ricci operator with eigen value \(2n+1.\)

中文翻译：

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Sasaki–Kenmotsu 流形上的某些向量场

摘要

本文的目的是研究 Sasaki-Kenmotsu 流形上的 Ricci 孤子。结果表明，如果特征向量场\(\xi\)和\(\psi\)是作为 Ricci 孤子的 Sasaki-Kenmotsu 度量上的循环扭转形成向量场，则\(\xi\)和\ (\psi\)是并发向量场和杀伤向量场。我们对承认全纯平面共角向量\((HPCV)\)场的Sasaki-Kenmotsu流形进行分类和表征。此外，我们还证明Sasaki-Kenmotsu 流形上的\(HPCV\)场是螺线管场。此外，在承认\(HPCV\)场\(V\)且\(\phi V\neq 0\) 的 Sasaki –Kenmotsu 流形中，\(HPCV\)场是具有特征值的 Ricci 算子的特征向量\(2n+1。\)