2017/04/11 by José N. V. Gomes, Gomes, José N. V., Manoel V. M. Neto +1
Mathematics · Physics and Astronomy · #53A30 #53C12 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Primary 53C15 #Secondary 53C24
paper · pdf · doi:10.48550/arxiv.1704.03130
openalex publication_date 2017/04/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we study a Ricci-Hessian type manifold (\BbbM,g,φ,f,λ) which is closely related to the construction of almost Ricci soliton realized as a warped product. We classify certain classes of the Ricci-Hessian type manifolds and derive some implications for almost Ricci solitons and generalized m--quasi-Einstein manifolds. We consider two complementary cases: ∇ f and ∇φ are linearly independent in C^∞(\BbbM)--module \mathfrakX(\BbbM); and ∇ f=h∇φ for a smooth function h on \BbbM. In the first case we show that the vector field ∇λ belongs to the C^∞(\BbbM)--module generated by ∇ f and ∇φ, while in the second case, under additional hypothesis, the manifold is, around any regular point of f, locally isometric to a warped product.