Papers by Dr. Sudhakar Chaubey
Mathematics
This paper aims to explore the metallic structure J2=pJ+qI, where p and q are natural numbers, us... more This paper aims to explore the metallic structure J2=pJ+qI, where p and q are natural numbers, using complete and horizontal lifts on the tangent bundle TM over almost quadratic ϕ-structures (briefly, (ϕ,ξ,η)). Tensor fields F˜ and F* are defined on TM, and it is shown that they are metallic structures over (ϕ,ξ,η). Next, the fundamental 2-form Ω and its derivative dΩ, with the help of complete lift on TM over (ϕ,ξ,η), are evaluated. Furthermore, the integrability conditions and expressions of the Lie derivative of metallic structures F˜ and F* are determined using complete and horizontal lifts on TM over (ϕ,ξ,η), respectively. Finally, we prove the existence of almost quadratic ϕ-structures on TM with non-trivial examples.
Konuralp Journal of Mathematics (KJM), Apr 15, 2020
The object of the present paper is to study the properties of three-dimensional Lorentzian concir... more The object of the present paper is to study the properties of three-dimensional Lorentzian concircular structure ((LCS) 3-)manifolds admitting the almost conformal η-Ricci solitons and gradient shrinking η-Ricci solitons. It is proved that an (LCS) 3-manifold with either an almost conformal η-Ricci soliton or a gradient shrinking η-Ricci soliton is a quasi-Einstein manifold. Also, the example of an almost conformal η-Ricci soliton in an (LCS) 3-manifold is provided in the region where (LCS) 3-manifold is expanding.
Filomat, 2012
Yano [1] defined and studied semi-symmetric metric connection in a Riemannian manifold and this w... more Yano [1] defined and studied semi-symmetric metric connection in a Riemannian manifold and this was extended by De and Senguta [8] and many other geometers. Recently, the present authors [3], [5] defined semi-symmetric non-metric connections in an almost contact metric manifold. In this paper, we studied some properties of a semi-symmetric non-metric connection in a Kenmotsu manifold.
Research in mathematics, Aug 13, 2023
Surveys in Mathematics and its Applications, Dec 3, 2018
Konuralp Journal of Mathematics (KJM), Apr 15, 2018
The present paper deals with the study of Ricci soliton on weak symmetries of almost Kenmotsu (κ,... more The present paper deals with the study of Ricci soliton on weak symmetries of almost Kenmotsu (κ, µ, ν)−space and its geometric properties. Also, we obtain the condition for Ricci soliton on weakly symmetric and weakly Ricci symmetric almost Kenmotsu (κ, µ, ν)−space with the tensor field £ ξ g + 2S is parallel to be shrinking, steady and expanding respectively.
Afrika Matematika, Sep 19, 2018
The object of the present paper is to study the properties of N (k)-quasi Einstein manifolds. The... more The object of the present paper is to study the properties of N (k)-quasi Einstein manifolds. The existence of some classes of such manifolds are proved by constructing physical and geometrical examples. It is also shown that the characteristic vector field of the manifold is a unit parallel vector field as well as Killing vector field.
International Journal of Geometric Methods in Modern Physics, Mar 25, 2023
In this paper, we characterize the [Formula: see text]-Einstein cosymplectic manifolds with the g... more In this paper, we characterize the [Formula: see text]-Einstein cosymplectic manifolds with the gradient Einstein solitons and the conformal vector fields. It is proven that if an [Formula: see text]-Einstein cosymplectic manifold [Formula: see text] of dimension [Formula: see text] with [Formula: see text] admits a gradient Einstein soliton, then either [Formula: see text] is Ricci flat or the gradient of Einstein potential function is pointwise collinear with the Reeb vector field of [Formula: see text]. Also, we prove that if [Formula: see text] admits a conformal vector field [Formula: see text], then either [Formula: see text] is Ricci flat or [Formula: see text] is homothetic. We also establish that a conformal vector field [Formula: see text] on [Formula: see text] is a strict infinitesimal contact transformation, provided the scalar curvature of [Formula: see text] is constant. Finally, the non-trivial examples of cosymplectic manifolds admitting the gradient Einstein solitons are given.
Axioms
The aim of this paper is to characterize a Riemannian 3-manifold M3 equipped with a semi-symmetri... more The aim of this paper is to characterize a Riemannian 3-manifold M3 equipped with a semi-symmetric metric ξ-connection ∇˜ with ρ-Einstein and gradient ρ-Einstein solitons. The existence of a gradient ρ-Einstein soliton in an M3 admitting ∇˜ is ensured by constructing a non-trivial example, and hence some of our results are verified. By using standard tensorial technique, we prove that the scalar curvature of (M3,∇˜) satisfies the Poisson equation ΔR=4(2−σ−6ρ)ρ.
Mathematics
The characterization of Finsler spaces with Ricci curvature is an ancient and cumbersome one. In ... more The characterization of Finsler spaces with Ricci curvature is an ancient and cumbersome one. In this paper, we have derived an expression of Ricci curvature for the homogeneous generalized Matsumoto change. Moreover, we have deduced the expression of Ricci curvature for the aforementioned space with vanishing the S-curvature. These findings contribute significantly to understanding the complex nature of Finsler spaces and their curvature properties.
In this paper, we consider an η-Ricci soliton on the (LCS)n-manifolds (M,φ, ξ, η, g) satisfying c... more In this paper, we consider an η-Ricci soliton on the (LCS)n-manifolds (M,φ, ξ, η, g) satisfying certain curvature conditions likes: R(ξ,X) · S = 0 and W2(ξ,X) · S = 0. We show that on the (LCS)n-manifolds (M,φ, ξ, η, g), the existence of η-Ricci soliton implies that (M, g) is a quasi-Einstein. Further, we discuss the existence of Ricci solitons with the potential vector field ξ. In the end, we construct the non-trivial examples of η-Ricci solitons on the (LCS)n-manifolds.
Arab Journal of Mathematical Sciences, 2021
PurposeThe central idea of this research article is to examine the characteristics of Clairaut su... more PurposeThe central idea of this research article is to examine the characteristics of Clairaut submersions from Lorentzian trans-Sasakian manifolds of type (α, β) and also, to enhance this geometrical analysis with some specific cases, namely Clairaut submersion from Lorentzian α-Sasakian manifold, Lorentzian β-Kenmotsu manifold and Lorentzian cosymplectic manifold. Furthermore, the authors discuss some results about Clairaut Lagrangian submersions whose total space is a Lorentzian trans-Sasakian manifolds of type (α, β). Finally, the authors furnished some examples based on this study.Design/methodology/approachThis research discourse based on classifications of submersion, mainly Clairaut submersions, whose total manifolds is Lorentzian trans-Sasakian manifolds and its all classes like Lorentzian Sasakian, Lorenztian Kenmotsu and Lorentzian cosymplectic manifolds. In addition, the authors have explored some axioms of Clairaut Lorentzian submersions and illustrates our findings wit...
Journal of Mathematical Physics, 2021
This paper deals with the study of perfect fluid spacetimes. It is proven that a perfect fluid sp... more This paper deals with the study of perfect fluid spacetimes. It is proven that a perfect fluid spacetime is Ricci recurrent if and only if the velocity vector field of perfect fluid spacetime is parallel and α = β. In addition, in a stiff matter perfect fluid Yang pure space with p + σ ≠ 0, the integral curves generated by the velocity vector field are geodesics. Moreover, it is shown that in a generalized Robertson–Walker perfect fluid spacetime, the Weyl tensor is divergence-free and the gradient of the potential function of the concircular vector field is pointwise collinear with the velocity vector field of perfect fluid spacetime. We also characterize the perfect fluid spacetimes whose Lorentzian metrics are Yamabe and gradient Yamabe solitons, respectively.
Universal Journal of Mathematics and Applications, 2020
The aim of the present paper is to study the properties of Riemannian manifolds equipped with a p... more The aim of the present paper is to study the properties of Riemannian manifolds equipped with a projective semi-symmetric connection.
Mathematics
The curvature characteristics of particular classes of Finsler spaces, such as homogeneous Finsle... more The curvature characteristics of particular classes of Finsler spaces, such as homogeneous Finsler spaces, are one of the major issues in Finsler geometry. In this paper, we have obtained the expression for S-curvature in homogeneous Finsler space with a generalized Matsumoto metric and demonstrated that the homogeneous generalized Matsumoto space with isotropic S-curvature has to vanish the S-curvature. We have also derived the expression for the mean Berwald curvature by using the formula of S-curvature.
Physica Scripta
The main aim of this manuscript is to characterize the general relativistic spacetimes with Ricci... more The main aim of this manuscript is to characterize the general relativistic spacetimes with Ricci and gradient Ricci solitons. It is proven that if the metric of a general relativistic spacetime (M 4, ξ) admitting a special unit timelike vector field ξ is an almost Ricci soliton (g, ξ, λ), then (M 4, ξ) is a perfect fluid spacetime, and almost Ricci soliton (g, ξ, λ) on (M 4, ξ) becomes shrinking Ricci soliton. We prove that a general relativistic perfect fluid spacetime equipped with a special unit timelike vector field together with a Ricci soliton is an Einstein spacetime. In this sequel, we also prove that the Ricci soliton is shrinking, soliton vector field is Killing and the scalar curvature of the perfect fluid spacetime is constant. It is proven that a general relativistic perfect fluid spacetime together with a Ricci soliton is a generalized Robertson-Walker (GRW) spacetime. The existence of gradient Ricci solitons on general relativistic spacetimes are established. We also...
Filomat
In this manuscript, we give the definition of Riemannian concircular structure manifolds. Some ba... more In this manuscript, we give the definition of Riemannian concircular structure manifolds. Some basic properties and integrability condition of such manifolds are established. It is proved that a Riemannian concircular structure manifold is semisymmetric if and only if it is concircularly flat. We also prove that the Riemannian metric of a semisymmetric Riemannian concircular structure manifold is a generalized soliton. In this sequel, we show that a conformally flat Riemannian concircular structure manifold is a quasi-Einstein manifold and its scalar curvature satisfies the partial differential equation ?r = ?2r/?t2 + ?(n?1)?r/?t. To validate the existence of Riemannian concircular structure manifolds, we present some non-trivial examples. In this series, we show that a quasi-Einstein manifold with a divergence free concircular curvature tensor is a Riemannian concircular structure manifold.
Zurnal matematiceskoj fiziki, analiza, geometrii
Mathematics
The target of the current research article is to investigate the solitonic attributes of relativi... more The target of the current research article is to investigate the solitonic attributes of relativistic magneto-fluid spacetime (MFST) if its metrics are Ricci–Yamabe soliton (RY-soliton) and gradient Ricci–Yamabe soliton (GRY-soliton). We exhibit that a magneto-fluid spacetime filled with a magneto-fluid density ρ, magnetic field strength H, and magnetic permeability μ obeys the Einstein field equation without the cosmic constant being a generalized quasi-Einstein spacetime manifold (GQE). In such a spacetime, we obtain an EoS with a constant scalar curvature R in terms of the magnetic field strength H and magnetic permeability μ. Next, we achieve some cauterization of the magneto-fluid spacetime in terms of Ricci–Yamabe solitons with a time-like torse-forming vector field ξ and a φ(Ric) vector field. We establish the existence of a black hole in the relativistic magneto-fluid spacetime by demonstrating that it admits a shrinking Ricci–Yamabe soliton and satisfies the time-like energ...
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Papers by Dr. Sudhakar Chaubey