Browsing by Author "Arindam Bhattacharyya"

Now showing 1 - 9 of 9

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.
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.
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.
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 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 warped products with a quarter-symmetric connection
(World Scientific Publishing Co. Pte Ltd, 2017) Sampa Pahan; Buddhadev Pal; Arindam Bhattacharyya
This paper characterizes the warping functions for a multiply generalized Robertson-Walker space-time to get an Einstein space M with a quarter-symmetric connection for different dimensions of M (i.e. (1). dim M = 2, (2). dim M ≥ 3) when all the fibers are Ricci flat. Then we have also computed the warping functions for a Ricci flat Einstein multiply warped product spaces M with a quarter-symmetric connection for different dimensions of M (i.e. (1). dim M = 2, (2). dim M = 3, (3). dim M ≥ 4) and all the fibers are Ricci flat. In the last section, we have given two examples of multiply generalized Robertson-Walker space-time with respect to quarter-symmetric connection. © 2017 World Scientific Publishing Company.
On nearly quasi-einstein warped products
(Institute of Mathematics, 2016) Buddhadev Pal; Arindam Bhattacharyya
We study nearly quasi-Einstein warped product manifolds for arbitrary dimension n ≥ 3. In the last section we also give an example of warped product on nearly quasi-Einstein manifold. © 2016, Institute of Mathematics. All rights reserved.
On some classes of mixed-super quasi-Einstein manifolds
(Sapientia University, 2016) Santu Dey; Buddhadev Pal; Arindam Bhattacharyya
Quasi-Einstein manifold and generalized quasi-Einstein manifold are the generalizations of Einstein manifold. The purpose of this paper is to study the mixed super quasi-Einstein manifold which is also the generalizations of Einstein manifold satisfying some curvature conditions. We de fine both Riemannian and Lorentzian doubly warped product on this manifold. Finally, we study the completeness properties of doubly warped products on MS(QE)4 for both the Riemannian and Lorentzian cases.