https://neckpinch.com/authors/hemangi-madhusudan-shah/New arXiv papers by Hemangi Madhusudan Shah, from Neckpinch Tue, 03 Nov 2026 07:15:30 GMT https://arxiv.org/abs/2607.22394arxiv: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://arxiv.org/abs/2606.14336arxiv:2606.14336Fri, 12 Jun 2026 00:00:00 GMTShubham Yadav, Hemangi Madhusudan Shah — This article explores to what extent the geometry of gradient Ricci solitons extends to non-gradient Ricci solitons. The primary tool is the energy function E of the soliton. We study consequences of various bounds on E. Under mild assumptions on the scalar curvature, we prove a weighted L¹-Liouville type theorem for both the usual Laplacian and the drifted Laplacian Δ_V associated to soliton vector field V, the former of which implies that Ricci solitons with bounded energy function have at most one nonparabolic end. Finally, we show that the measure e^(−E) d Vol_g is finite for complete shrinking Ricci solitons, partially generalizing a result of Aaron Naber. As a consequence, non-gradient shrinking Ricci solitons also have finite fundamental groups, as in the gradient case.Ricci solitonsScalar curvature https://arxiv.org/abs/2512.17704arxiv: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 https://arxiv.org/abs/2305.06597arxiv:2305.06597Thu, 11 May 2023 00:00:00 GMTParitosh Ghosh, Hemangi Madhusudan Shah, Arindam Bhattacharyya — In this research, we study the nature of η-Einstein and gradient η-Einstein soliton in the framework of almost coKähler manifolds and (κ, μ)-almost coKähler manifolds. We find some expressions for scalar curvature of the almost coKähler manifold admitting η-Einstein soliton in various cases. We also prove that if a (κ, μ)-almost coKähler manifold admits a gradient η-Einstein soliton, then either the manifold is coKähler, or N(κ)-almost coKahler, or the soliton is trivial. We present an example which validates our results. Finally, we investigate the asymptotically harmonic manifolds admitting non-trivial Ricci solitons and show that they exhibit rigid behavior if for example, scalar curvature attains maximum.Ricci solitonsAlmost & η-Ricci solitonsKähler geometryScalar curvature