https://neckpinch.com/authors/dibakar-dey/New arXiv papers by Dibakar Dey, from Neckpinch Tue, 03 Nov 2026 08:41:12 GMT https://neckpinch.com/papers/2109.04220/arxiv:2109.04220Tue, 24 Aug 2021 00:00:00 GMTDibakar Dey — It is well known that a unit sphere admits Sasakian 3-structure. Also, Sasakian manifolds are locally isometric to a unit sphere under several curvature and critical conditions. So, a natural question is: Does there exist any curvature or critical condition under which a Sasakian 3-manifold represents a geometrical object other than the unit sphere? In this regard, as an extension of the ∗-Ricci soliton, the notion of ∗-Ricci-Yamabe soliton is introduced and studied on two classes contact metric manifolds. A (2n + 1)-dimensional non-Sasakian N(k)-contact metric manifold admitting ∗-Ricci-Yamabe soliton is completely classified. Further, it is proved that if a Sasakian 3-manifold M admits ∗-Ricci-Yamabe soliton (g,V,λ,α,β) under certain conditions on the soliton vector field V, then M is ∗-Ricci flat, positive Sasakian and the transverse geometry of M is Fano. In addition, the Sasakian 3-metric g is homothetic to a Berger sphere and the soliton is steady. Also, the potential vector field V is an infinitesimal automorphism of the contact metric structure.Ricci solitonsRicci-flat & Calabi–YauAlmost & η-Ricci solitons3-manifoldsKähler geometrySasakian & contact geometry