The $k$-almost Ricci solitons and contact geometry
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The aim of this article is to study the $k$-almost Ricci soliton and $k$-almost gradient Ricci soliton on contact metric manifold. First, we prove that if a compact $K$-contact metric is a $k$-almost gradient Ricci soliton, then it is isometric to a unit sphere $S^{2n+1}$. Next, we extend this result on a compact $k$-almost Ricci soliton when the flow vector field $X$ is contact. Finally, we study some special types of $k$-almost Ricci solitons where the potential vector field $X$ is point wise collinear with the Reeb vector field $\xi$ of the contact metric structure.
Abstract
The aim of this article is to study the $k$-almost Ricci soliton and $k$-almost gradient Ricci soliton on contact metric manifold. First, we prove that if a compact $K$-contact metric is a $k$-almost gradient Ricci soliton, then it is isometric to a unit sphere $S^{2n+1}$. Next, we extend this result on a compact $k$-almost Ricci soliton when the flow vector field $X$ is contact. Finally, we study some special types of $k$-almost Ricci solitons where the potential vector field $X$ is point wise collinear with the Reeb vector field $\xi$ of the contact metric structure.
참고문헌 (20)
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