https://neckpinch.com/authors/ahmet-umut-corapl/New arXiv papers by Ahmet Umut Çoraplı, from Neckpinch Tue, 03 Nov 2026 08:41:12 GMT https://neckpinch.com/papers/2508.12098/arxiv:2508.12098Sat, 16 Aug 2025 00:00:00 GMTAhmet Umut Çoraplı, Burcu Bektaş Demirci, Nurettin Cenk Turgay — In this paper, we study hypersurfaces in the product spaces ℚ_ε³ × ℝ for which the tangential component T of the vector field ∂/∂t is a principal direction, where ℚ_ε³ denotes the three-dimensional non-flat Riemannian space form with sectional curvature ε= ± 1, and ∂/∂t is the unit vector field tangent to the ℝ-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 T. 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.Ricci solitonsAlmost & η-Ricci solitons3-manifoldsSphere theorems