论文标题

在非梯度$(m,ρ)$ - 准内施坦联系公制歧管上

On non-gradient $(m,ρ)$-quasi-Einstein contact metric manifolds

论文作者

Patra, Dhriti Sundar, Rovenski, Vladimir

论文摘要

许多作者在(几乎)接触几何形状的框架内研究了Ricci孤子及其类似物。在本文中,我们彻底研究了接触度量歧管上的$(M,ρ)$ -Quasi-Einstein结构。首先,我们证明,如果a $ k $ - contact或sasakian歧管$ m^{2n+1} $承认封闭的$(m,ρ)$ - quasi-einstein结构,那么它是恒定标量弯曲的爱因斯坦流形的,即恒定标量弯曲的$ 2n(2n+1)$,对于特定的情况 - lotancy of-sasakiian of the Is-sasak $($ conterconty of-sasak $(k) Euclidean Space $ \ rr^{n+1} $和一个球体$ s^n $的常数曲率$ 4 $。接下来,我们证明,如果紧凑型联系人或$ h $ -contact公制歧管承认$(m,ρ)$ - Quasi-Einstein结构,其潜在的矢量字段$ v $是对Reeb vector Field的界面,那么它是$ K $ -CONTACT $ -CONTACT $η$ -Einenstein歧管。

Many authors have studied Ricci solitons and their analogs within the framework of (almost) contact geometry. In this article, we thoroughly study the $(m,ρ)$-quasi-Einstein structure on a contact metric manifold. First, we prove that if a $K$-contact or Sasakian manifold $M^{2n+1}$ admits a closed $(m,ρ)$-quasi-Einstein structure, then it is an Einstein manifold of constant scalar curvature $2n(2n+1)$, and for the particular case -- a non-Sasakian $(k,μ)$-contact structure -- it is locally isometric to the product of a Euclidean space $\RR^{n+1}$ and a sphere $S^n$ of constant curvature $4$. Next, we prove that if a compact contact or $H$-contact metric manifold admits an $(m,ρ)$-quasi-Einstein structure, whose potential vector field $V$ is collinear to the Reeb vector field, then it is a $K$-contact $η$-Einstein manifold.

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