https://neckpinch.com/authors/manoel-v-m-neto/New arXiv papers by Manoel V. M. Neto, from Neckpinch Tue, 10 Nov 2026 04:10:28 GMT https://neckpinch.com/papers/1704.03130/arxiv:1704.03130Tue, 11 Apr 2017 00:00:00 GMTJosé N. V. Gomes, Manoel V. M. Neto — 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 X(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.Ricci solitonsEinstein metricsAlmost & η-Ricci solitonsRotational symmetry & warped products