Almost Ricci Solitons on Class Hypersurfaces of Product Spaces
In this paper, we study hypersurfaces in the product spaces for which the tangential component of the vector field is a principal direction, where denotes the three-dimensional non-flat Riemannian space form with sectional curvature , and is the unit vector field tangent to the -factor. We obtain a local classification of hypersurfaces with three distinct principal curvatures satisfying specific functional relations. Then, we determine the necessary and sufficient conditions for such hypersurfaces to admit an almost Ricci soliton structure with potential vector field . Finally, we prove that the only hypersurfaces admitting such solitons are rotational, by showing that the constructed examples with three distinct principal curvatures do not admit almost Ricci solitons.