Almost hyperbolic Ricci solitons on almost co-Ka¨hler manifolds
DOI:
https://doi.org/10.31489/2026m3/74-85Keywords:
hyperbolic Ricci solitons, torse-forming vector fields, conformal Killing vector fields, Reeb vector field, Ricci-flat manifolds, contact metric geometry, almost co-Kähler manifolds, hyperbolic geometric flowAbstract
This research investigates almost hyperbolic Ricci solitons on almost co-K¨ahler manifolds, an important class of odd-dimensional manifolds closely related to Ka¨hler geometry. Motivated by recent developments in hyperbolic geometric flows and their self-similar solutions, we study the existence and geometric properties of almost hyperbolic Ricci solitons within the framework of almost co-Ka¨hler manifolds. First, we derive fundamental relations for almost hyperbolic Ricci solitons whose potential vector field is collinear with the Reeb vector field and obtain a differential equation governing the associated smooth function. We then examine almost hyperbolic Ricci solitons under several geometric conditions, including conformal Killing vector fields, torse-forming vector fields, Ricci bi-conformal vector fields, and (V (Ric))-vector fields. In each case, necessary conditions are established, leading to characterization results and Einstein-type properties of the underlying manifolds. In particular, we obtain criteria under which an almost co-Ka¨hler manifold is Einstein or Ricci-flat. Furthermore, for closed almost co-Ka¨hler manifolds admitting a (V (Ric))-vector field satisfying suitable trace conditions, we show that the manifold is Ricci-flat and the associated vector field is parallel. To illustrate the theoretical results, we construct two explicit three-dimensional examples of almost co-Ka¨hler manifolds admitting hyperbolic Ricci solitons.
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