Almost Ricci Solitons on Class \mathcal A Hypersurfaces of Product Spaces

2025/08/16 by Ahmet Umut Çoraplı, Çoraplı, Ahmet Umut, Burcu Bektaş Demirci +3
Mathematics · Physics and Astronomy · #53A10 #53C42 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Mathematical Physics (math-ph)

paper · pdf · doi:10.48550/arxiv.2508.12098

openalex publication_date 2025/08/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Citations

• On a Class of Gradient Almost Ricci Solitons
• Classification of Ricci solitons on Euclidean hypersurfaces
• Ricci solitons and concurrent vector fields
• Three-dimensional Lorentzian homogeneous Ricci solitons
• The entropy formula for the Ricci flow and its geometric applications

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