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<p>We study geometric aspects of an almost conformal Ricci soliton and an almost conformal gradient Ricci soliton on K-contact manifolds. Among others, we first obtain the nature of almost conformal Ricci soliton under the conditions: (i) the potential vector field is a contact vector field, and (ii) the potential vector field is pointwise collinear with the Reeb vector field ξ<i>.</i> Moreover, we present an example of almost conformal Ricci soliton on a K-contact manifold with potential vector field as a contact vector field. We also find a necessary and sufficient condition for the existence of cyclic Ricci tensor on a K-contact manifold. Further, we give a necessary and sufficient condition for the potential vector field <i>V</i> of a conformal Ricci soliton to be Jacobi along ξ on the K-contact η-Einstein manifold, and study the nature of almost conformal Ricci soliton on the K-contact η -Einstein manifold when the potential vector field is a conformal vector field. Finally, we prove that if a complete K-contact metric is an almost conformal gradient Ricci soliton, then the manifold is isometric to a hyperbolic space <i>H</i><sup>2<i>n</i>+1</sup>(<i>→</i>1)<i>.</i></p>

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Geometry of Almost Conformal Ricci Solitons on K-Contact Manifolds

  • 期刊论文

  • 发表日期：

    2025年12月12日

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  • Akhilesh Yadav,
  • Tarun Saxena

摘要

We study geometric aspects of an almost conformal Ricci soliton and an almost conformal gradient Ricci soliton on K-contact manifolds. Among others, we first obtain the nature of almost conformal Ricci soliton under the conditions: (i) the potential vector field is a contact vector field, and (ii) the potential vector field is pointwise collinear with the Reeb vector field ξ. Moreover, we present an example of almost conformal Ricci soliton on a K-contact manifold with potential vector field as a contact vector field. We also find a necessary and sufficient condition for the existence of cyclic Ricci tensor on a K-contact manifold. Further, we give a necessary and sufficient condition for the potential vector field V of a conformal Ricci soliton to be Jacobi along ξ on the K-contact η-Einstein manifold, and study the nature of almost conformal Ricci soliton on the K-contact η -Einstein manifold when the potential vector field is a conformal vector field. Finally, we prove that if a complete K-contact metric is an almost conformal gradient Ricci soliton, then the manifold is isometric to a hyperbolic space H2n+1(→1).