Browsing by Author "Buddhadev Pal"

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A family of multiply warped product semi-riemannian einstein metrics
(American Institute of Mathematical Sciences, 2020) Buddhadev Pal; Pankaj Kumar
In this paper, we characterize multiply warped product semi - Riemannian manifolds when the base is conformal to an n-dimensional pseudo-Euclidean space. We prove some conditions on warped product semi- Riemannian manifolds to be an Einstein manifold which is invariant under the action of an (n − 1)-dimensional translation group. After that we apply this result for the case of Ricci-flat multiply warped product space when the fibers are Ricci-flat. We also discuss the existence of infinitely many Ricci-flat multiply warped product spaces under the same action with null like vector. © 2020 American Institute of Mathematical Sciences. All rights reserved.
A new way to study on generalized Friedmann–Robertson–Walker spacetime
(Springer, 2022) Nandan Bhunia; Buddhadev Pal; Arindam Bhattacharyya
In this paper, we study the generalized Friedmann–Robertson–Walker spacetime in a new way. We know that the generalized Friedmann-Robertson-Walker metric and solutions of the Einstein field equations can be expressed in terms of Lorentzian warped products. We consider a multiply warped product metric of the generalized Friedmann-Robertson-Walker spacetime of type M¯=B×h1F1×h2F2 with the warping functions h1, h2 associated to the submanifolds F1, F2 with dimensions n1, n2, respectively and the submanifold F1 is conformal to (Rn1,g), a pseudo-Euclidean space. Then we show that the Einstein equations G¯AB=-κ¯g¯AB on (M¯ , g¯) with a cosmological constant κ¯ is reduced to the Einstein equations Gij=-κ2g2ij on the submanifold (F2, g2) with the cosmological constant κ2. Furthermore, we consider some black hole solutions as typical examples. Then we derive the corresponding Einstein equations and the reduced Einstein equations for each black hole solution. © 2022, Indian Association for the Cultivation of Science.
Almost Ricci-Bourguignon soliton on warped product space
(Elsevier Ltd, 2023) Santosh Kumar; Pankaj Kumar; Buddhadev Pal
The purpose of this article is to study the almost Ricci-Bourguignon soliton on warped product space. Some results for solenoidal and concurrent vector fields are obtained on warped product space with almost Ricci-Bourguignon soliton. We provide the relation between the warped manifold and its base manifold (fiber manifold) for an almost Ricci-Bourguignon soliton. We also generalize the Bochner formula in warped product space. Next, we study the Riemannian map whose total manifold admits an almost Ricci-Bourguignon soliton. We find the condition for a kernel of Riemannian map to become an almost Ricci-Bourguignon soliton. Moreover, we give an example for almost Ricci-Bourguignon soliton on warped product space. © 2023 Polish Scientific Publishers
An introduction to gradient solitons on statistical Poisson manifold and perfect fluid Poisson manifold
(Elsevier B.V., 2024) Buddhadev Pal; Ram Shankar Chaudhary
In this article, we introduce the idea of statistical Poisson manifold and perfect fluid Poisson manifold. Then, we investigate the well known almost solitons like Ricci soliton, Yamabe solitons or Einstein solitons on Poisson manifold and discuss the statistical structures. Next, we find a volume formula of the Poisson manifold and discuss the bounds of |Ric|2 for gradient solitons. Afterward, we study statistical structure on a perfect fluid Poisson manifold. Then, we obtain the volume formula and bounds of |Ric|2 for perfect fluid Poisson manifold. © 2023 Elsevier B.V.
Characterization of Einstein Poisson warped product space
(Springer Science and Business Media Deutschland GmbH, 2022) Buddhadev Pal; Pankaj Kumar
In this article, we study the problem of the existence and nonexistence of warping function associated with constant scalar curvature on pseudo-Riemannian Poisson warped product space under the assumption that fiber space has constant scalar curvature. We characterize the warping function on Einstein Poisson warped space by taking the various dimensions of base space B (i.e; (1). dimB= 1 , (2). dimB≥ 2). © 2022, African Mathematical Union and Springer-Verlag GmbH Deutschland, ein Teil von Springer Nature.
Characterization of Kenmotsu manifolds with a generalized symmetric metric connection
(University of Nis, 2025) Oǧuzhan Bahadır; Mohammad Nazrul Islam Khan; Santosh Kumar; Buddhadev Pal
The objective of the present findings is to analyze Kenmotsu manifolds by using (α, β) type generalized symmetric metric connection. The characterization of Kenmotsu manifold by using certain curvature properties corresponding to the generalized symmetric metric connection is investigated. In the end, an example of Kenmotsu manifold with the generalized symmetric metric connection admitting Q tensor and Weyl conformal curvature tensor is constructed by using partial differential equations. © 2025, University of Nis. All rights reserved.
Characterization of proper curves and proper helix lying on S21 (r)
(Hacettepe University, 2022) Buddhadev Pal; Santosh Kumar
In this paper, we analyse the proper curve γ(s) lying on the pseudo-sphere. We develop an orthogonal frame {V1, V2, V3 } along the proper curve, lying on pseudosphere. Next, we find the condition for γ(s) to become Vk − slant helix in Minkowski space. Moreover, we find another curve β(¯s) lying on pseudosphere or hyperbolic plane heaving V2 =¯V2 for which {¯V1,¯V2,¯V3 }, an orthogonal frame along β(¯s). Finally, we find the condition for curve γ(s) to lie in a plane. © 2022, Hacettepe University. All rights reserved.
Characterization on a Non-flat Riemannian Manifold
(Springer India, 2018) Sampa Pahan; Buddhadev Pal; Arindam Bhattacharyya
In this paper we study characterizations of odd and even dimensional pseudo generalized quasi Einstein manifold and we give three and four dimensional examples (both Riemannian and Lorentzian) of pseudo generalized quasi Einstein manifold to show the existence of such manifold. Also in the last section we give the examples of warped product on pseudo generalized quasi Einstein manifold. © 2016, The National Academy of Sciences, India.
Compact Einstein multiply warped product space with nonpositive scalar curvature
(World Scientific Publishing Co. Pte Ltd, 2019) Buddhadev Pal; Pankaj Kumar
In this paper, we characterize the Einstein multiply warped product space with nonpositive scalar curvature. As a result, it is shown that, if M is Einstein multiple-warped product spaces with compact base and nonpositive scalar curvature, then M is simply a Riemannian manifold. Next, we apply our result on Generalized Robertson-Walker space-time and Generalized Friedmann-Robertson-Walker space-time. © 2019 World Scientific Publishing Company.
CONFORMAL MAPPINGS OF GENERALIZED QUASI-EINSTEIN MANIFOLDS ADMITTING SPECIAL VECTOR FIELDS
(Canadian University of Dubai, 2020) Santu Dey; Buddhadev Pal; Arindam Bhattacharyya
Einstein manifolds form a natural subclass of the class of quasi-Einstein manifolds and plays an important role in geometry as well as in general theory of relativity. In this work, we investigate conformal mappings of generalized quasi-Einstein manifolds. We consider a conformal mapping between two generalized quasi-Einstein manifolds Vn and¯Vn . We also find some properties of this transformation from Vn to¯Vn and some theorems are proved. Considering this mapping, we examine some properties of these manifolds. Af-ter that, we also study some special vector fields under this mapping on these manifolds and some theorems about them are proved. © 2020, Canadian University of Dubai. All rights reserved.
Einstein Poisson warped product space
(IOP Publishing Ltd, 2021) Buddhadev Pal; Pankaj Kumar
In this paper, we provide some results on Poisson manifold (M, Π) with contravariant Levi–Civita connection D associated to pair (Π, g). We introduce the notion of Einstein Poisson warped product space (M = B ×f F, Π, gf) (where Π = Π1 + Π2). Moreover, we show that if M is an Einstein Poisson warped product space with nonpositive scalar curvature and compact base B, J1 is a field endomorphism on T∗B satisfies J12 = I, then M is simply a Riemannian Poisson product. For a contravariant Lorentzian Poisson warped space (M = B ×f F, g, Π) (where B = I × R) one can determine contravariant Einstein equations and the cosmological constant Λ corresponding to the contravariant Einstein equation G = −Λg. Moreover, it is shown that Einstein equation G = −Λg, induces the contravariant Einstein equation GijF = −ΛFgijF with cosmological constant ΛF on fiber space (F, gF, ΠF). © 2021 IOP Publishing Ltd.
Einstein warped product spaces on Lie groups
(Universidad de la Frontera, 2022) Buddhadev Pal; Santosh Kumar; Pankaj Kumar
We consider a compact Lie group with bi-invariant metric, coming from the Killing form. In this paper, we study Einstein warped product space, M = M1 ×f1 M2 for the cases, (i) M1 is a Lie group (ii) M2 is a Lie group and (iii) both M1 and M2 are Lie groups. Moreover, we obtain the conditions for an Einstein warped product of Lie groups to become a simple product manifold. Then, we characterize the warping function for generalized Robertson-Walker spacetime, (M = I ×f1 G2, −dt2 + f12 g2) whose fiber G2, being semi-simple compact Lie group of dim G2 > 2, having bi-invariant metric, coming from the Killing form. © 2022 B. Pal et al. This open access article is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
Global view of curves lying on H02(−r) ⊂ E13
(Tbilisi Centre for Mathematical Sciences, 2023) Buddhadev Pal; Santosh Kumar
In this paper, we study the geometry of the proper curve and proper helix of order 2 lying on the hyperbolic plane H02(−r), globally from Minkowski space E13. We develop the Frenet frame (orthogonal frame) along the proper curve of order 2 using connection ∇̃ on E13 and connection ∇ on H02(−r). The Frenet frame for the proper curve and proper helix of order 2 depends on the curvature of the proper curve and proper helix of order 2 in the hyperbolic plane H02(−r). Finally, we find the condition for a proper curve of order 2 with non constant curvature to become a Vk−slant helix in E13 © 2023 authors. All rights reserved.
Gradient Ricci-Bourguignon solitons and applications
(Springer Science and Business Media Deutschland GmbH, 2025) Ram Shankar Chaudhary; Buddhadev Pal
In this article, we discuss the geometry of gradient Ricci-Bourguignon solitons (GRB) and then we characterize the general relativistic space-time with Ricci-Bourguignon (RB) and GRB solitons. First, we obtain the expression for the scalar curvature of a compact GRB soliton. Then, we prove that the gradient of the potential function of GRB soliton is bounded if its scalar curvature satisfies a boundedness condition. Then the Riemannian curvature of a 4-dimensional GRB soliton and its derivative are investigated whenever the Weyl tensor is harmonic. It is proven that if the potential vector field is torse-forming, then a compact RB soliton becomes perfect fluid space-time. We also discuss the bounds of the first eigenvalue of Laplacian. A volume formula for GRB soliton is obtained. Further, we study the application of conformal vector field on a RB soliton and obtain the expression for the Ricci curvature. Next, we find when RB soliton is expanding, shrinking and steady, if relativistic perfect fluid space-time admits a RB soliton with conformal vector field. We also construct a non-trivial example of GRB soliton equipped with a conformal potential vector field. © African Mathematical Union and Springer-Verlag GmbH Deutschland, ein Teil von Springer Nature 2025.
K-type slant helices on spacelike and timelike surfaces
(University of Tartu Press, 2021) Santosh Kumar; Buddhadev Pal
We have derived a necessary and sufficient condition for a non-null normal spacelike curve lying in a spacelike or a timelike surface (Formula presented) so that the curve becomes a K-type spacelike slant helix with (Formula presented). We have used Darboux frame to define necessary and sufficient conditions. An example is given for a 1-type spacelike slant helix having a spacelike normal and a timelike binormal. © 2021, University of Tartu Press. All rights reserved.
Multiply warped product on quasi-einstein manifold with a semi-symmetric non-metric connection
(College of Nyregyhaza, 2017) Sampa Pahan; Buddhadev Pal; Arindam Bhattacharyya
In this paper, we have studied warped products and multiply warped product on quasi-Einstein manifold with semi-symmetric non-metric connection. Then we have applied our results to generalized Robertson-Walker space times with a semi-symmetric non-metric connection.
Multiply warped products as quasi-Einstein manifolds with a quarter-symmetric connection
(EUT Edizioni Universita di Trieste, 2016) Sampa Pahan; Buddhadev Pal; Arindam Bhattacharyya
In this paper we study warped products and multiply warped products on quasi-Einstein manifolds with a quarter-symmetric connection. Then we apply our results to generalize Robertson-Walker spacetime with a quarter-symmetric connection.
On a non flat Riemannian warped product manifold with respect to quarter-symmetric connection
(Sciendo, 2019) Buddhadev Pal; Santu Dey; Sampa Pahan
In this paper, we study generalized quasi-Einstein warped products with respect to quarter symmetric connection for dimension n ≥ 3 and Ricci-symmetric generalized quasi-Einstein manifold with quarter symmetric connection. We also investigate that in what conditions the generalized quasi-Einstein manifold to be nearly Einstein manifold with respect to quarter symmetric connection. Example of warped product on generalized quasi-Einstein manifold with respect to quarter symmetric connection are also discussed. © 2019 Buddhadev Pal et al., published by Sciendo 2019.
On compact super quasi-einstein warped product with nonpositive scalar curvature
(B. I. Verkin Institute for Low Temperature Physics and Engineering, 2017) Sampa Pahan; Buddhadev Pal; Arindam Bhattacharyya
This note deals with super quasi-Einstein warped product spaces. Here we establish that if M is a super quasi-Einstein warped product space with nonpositive scalar curvature and compact base, then M is simply a Riemannian product space. Next we give an example of super quasi-Einstein space-time. In the last section a warped product is defined on it. © K. Andreiev and I. Egorova, 2017.
On Einstein sequential warped product spaces
(B. I. Verkin Institute for Low Temperature Physics and Engineering, 2019) Sampa Pahan; Buddhadev Pal
In this paper, Einstein sequential warped product spaces are studied. Here we prove that if M is an Einstein sequential warped product space with negative scalar curvature, then the warping functions are constants. We find out some obstructions for the existence of such Einstein sequential warped product spaces. We also show that if (Formula Presented.) is a sequential warped product of a complete connected (n − 2)-dimensional Riemannian manifold M1 and one-dimensional Riemannian manifolds IM2 and IM with some certain conditions, then (M1, g1) becomes a (n − 2)- dimensional sphere of radius (Formula Presented.). Some examples of the Einstein sequential warped product space are given in Section 3. © Sampa Pahan and Buddhadev Pal, 2019.