https://neckpinch.com/authors/mohammad-aqib/New arXiv papers by Mohammad Aqib, from Neckpinch Tue, 03 Nov 2026 08:37:45 GMT https://neckpinch.com/papers/2607.22394/arxiv:2607.22394Fri, 24 Jul 2026 00:00:00 GMTHemangi Madhusudan Shah, Sharief Deshmukh, Mohammad Aqib — We study non-compact Ricci solitons of finite volume whose potential vector field has constant length. Under the assumptions that the scalar curvature is constant along the integral curves of the potential field and that a natural divergence term is integrable on the unit tangent bundle, we prove that such Ricci solitons are necessarily trivial. As applications, we characterise 3-dimensional Ricci solitons of constant length and of finite volume on almost α-cosymplectic manifolds. In fact, we show that these spaces are indeed compact quotients of Euclidean spaces. We also study complete, non-compact and finite volume contact metric manifolds in dimension 3 admitting a Reeb vector field as a Ricci soliton. We show that it is a compact spherical space form. We include some examples to illustrate the necessity of the finite-volume and constant-length assumptions.Ricci solitonsSphere theoremsScalar curvatureBoundaries & non-compactSasakian & contact geometry https://neckpinch.com/papers/2512.17704/arxiv:2512.17704Fri, 19 Dec 2025 00:00:00 GMTMohammad Aqib, Hemangi Madhusudan Shah, Dhriti Sundar Patra — In this paper, we revisit the study of almost Ricci-Bourguignon solitons by clarifying their position in the broader context of Einstein-type metrics. Motivated by known rigidity results for compact almost Ricci solitons, we aim to identify conditions under which a compact almost RB-soliton is trivial or exhibits special geometric properties. We compare our results with classical theorems of Barros and Ribeiro, and explain explicitly how our work extends or complements these earlier findings.Ricci solitonsAlmost & η-Ricci solitonsStability & uniqueness