Abstract

The purpose of this article is to investigate almost Ricci solitons on para- contact manifolds. We demonstrate that a gradient almost Ricci soliton whose metric is para-sasakian turns into Einstein with a constant scalar curvature −2n(2n + 1). Next, we get a few relationships between almost Ricci solitons and Ricci solitons on a K-paracontact manifold and its generalizations. Finally, some findings on para- contact manifolds and H-paracontact manifolds admitting an almost Ricci soliton with a potential vector field that is a pointwise collinear with the Reeb vector field are discovered.

中文翻译：

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准接触度量流形上几乎 Ricci 孤子的几何

摘要

本文的目的是研究准接触流形上的几乎 Ricci 孤子。我们证明了一个几乎是 Ricci 孤子的梯度，其度量是 para-sasakian 变成了具有恒定标量曲率- 2 n (2 n + 1) 的爱因斯坦。接下来，我们得到了K准接触流形上的几乎 Ricci 孤子和 Ricci 孤子之间的一些关系及其推广。最后，发现了准接触流形和H平行接触流形的一些发现，这些发现允许几乎 Ricci 孤子具有与 Reeb 矢量场点共线的势矢量场。