https://neckpinch.com/authors/romildo-pina/New arXiv papers by Romildo Pina, from Neckpinch Tue, 10 Nov 2026 04:10:28 GMT https://neckpinch.com/papers/2004.05053/arxiv:2004.05053Fri, 10 Apr 2020 00:00:00 GMTMarcio de Sousa, Paula Bonfim, Romildo Pina, Tiberio Martins — We study gradient Ricci solitons warped products whose base is the Euclidean space. We show that the warping functions of these manifolds are invariant under the (n-1)-dimensional translation group. We characterize the potential function when the torsion function depends only on one variable, which is a particular case of invariance by translation. From this study, we derive complete examples of expanding gradient Ricci solitons.Ricci solitonsRotational symmetry & warped products https://neckpinch.com/papers/1905.00068/arxiv:1905.00068Tue, 30 Apr 2019 00:00:00 GMTWillian Isao Tokura, Levi Adriano, Romildo Pina, Marcelo Barboza — In this paper, by slightly modifying Li-Yau's technique so that we can handle drifting Laplacians, we were able to find three different gradient estimates for the warping function, one for each sign of the Einstein constant of the fiber manifold. As an application, we exhibit a nonexistence theorem for gradient almost Ricci solitons possessing certain metric properties on the base of the warped product.Ricci solitonsAlmost & η-Ricci solitonsHarnack inequalitiesRotational symmetry & warped products