https://neckpinch.com/authors/krishnendu-de/New arXiv papers by Krishnendu De, from Neckpinch Tue, 03 Nov 2026 07:15:30 GMT https://arxiv.org/abs/2411.14988arxiv:2411.14988Fri, 22 Nov 2024 00:00:00 GMTK. De, U. C. De — In the present paper we study η-Ricci solitons on Kenmotsu 3-manifolds. Moreover, we consider η-Ricci solitons on Kenmotsu 3-manifolds with Codazzi type of Ricci tensor and cyclic parallel Ricci tensor. Beside these, we study φ-Ricci symmetric η-Ricci soliton on Kenmotsu 3-manifolds. Also Kenmotsu 3-manifolds satisfying the curvature condition R.R=Q(S,R) is considered. Finally, an example is constructed to prove the existence of a proper η-Ricci soliton on a Kenmotsu 3-manifold.Ricci solitonsAlmost & η-Ricci solitons3-manifoldsSasakian & contact geometry https://arxiv.org/abs/2406.16108arxiv:2406.16108Sun, 23 Jun 2024 00:00:00 GMTUday Chand De, Krishnendu De, Sinem Güler — In this article, we characterize a Lorentzian manifold 𝓜 with a semi-symmetric metric connection. At first, we consider a semi-symmetric metric connection whose curvature tensor vanishes and establish that if the associated vector field is a unit time-like torse-forming vector field, then 𝓜 becomes a perfect fluid spacetime. Moreover, we prove that if 𝓜 admits a semi-symmetric metric connection whose Ricci tensor is symmetric and torsion tensor is recurrent, then 𝓜 represents a generalized Robertson-Walker spacetime. Also, we show that if the associated vector field of a semi-symmetric metric connection whose curvature tensor vanishes is a f- Ric vector field, then the manifold is Einstein and if the associated vector field is a torqued vector field, then the manifold becomes a perfect fluid spacetime. Finally, we apply this connection to investigate Ricci solitons.Ricci solitonsPhysics https://arxiv.org/abs/2402.15846arxiv:2402.15846Sat, 24 Feb 2024 00:00:00 GMTKrishnendu De, Uday Chand De, Aydin Gezer — This article carries out the investigation of a three-dimensional Riemannian manifold N³ endowed with a semi-symmetric type non-metric connection. Firstly, we construct a non-trivial example to prove the existence of a semi-symmetric type non-metric connection on N³. It is established that a N³ with the semi-symmetric type non-metric connection, whose metric is a gradient Ricci soliton, is a manifold of constant sectional curvature with respect to the semi-symmetric type non-metric connection. Moreover, we prove that if the Riemannian metric of N³ with the semi-symmetric type non-metric connection is a gradient Yamabe soliton, then either N³ is a manifold of constant scalar curvature or the gradient Yamabe soliton is trivial with respect to the semi-symmetric type non-metric connection. We also characterize the manifold N³ with a semi-symmetric type non-metric connection whose metrics are Einstein solitons and m-quasi Einstein solitons of gradient type, respectively.Ricci solitonsAlmost & η-Ricci solitons3-manifoldsScalar curvature https://arxiv.org/abs/2402.15339arxiv:2402.15339Fri, 23 Feb 2024 00:00:00 GMTKrishnendu De, Mohammad Nazrul Islam Khan, Uday Chand De — In this article, we examine gradient type Ricci solitons and (m,τ)-quasi Einstein solitons in generalized Robertson-Walker (GRW) spacetimes. Besides, we demonstrate that in this scenario the GRW spacetime presents the Robertson-Walker (RW) spacetime and the perfect fluid (PF) spacetime presents the phantom era. Consequently, we show that if a GRW spacetime permits a gradient τ- Einstein solitons, then it also represents a PF spacetime under certain condition.Ricci solitonsAlmost & η-Ricci solitons