Papers by Arindam Bhattacharyya
Annals of the Alexandru Ioan Cuza University - Mathematics, 2014
In this paper we give characterizations of super quasi-Einstein manifold, mixed super quasi-Einst... more In this paper we give characterizations of super quasi-Einstein manifold, mixed super quasi-Einstein manifold and mixed generalized quasi-Einstein manifold for both even and odd dimensions.
A Non-Flat Riemannian Manifold Admitting Certain Vectors Fields
Journal of Dynamical Systems and Geometric Theories
Point in a polyhedron: A geometric perspective
Journal of Interdisciplinary Mathematics
Acta et Commentationes Universitatis Tartuensis de Mathematica
The objective of the present paper is to study N(k)-mixed generalized quasi-Einstein manifolds. W... more The objective of the present paper is to study N(k)-mixed generalized quasi-Einstein manifolds. We prove the existence of these manifolds. Later we establish some curvature properties of N(k)-mixed generalized quasi-Einstein manifolds under certain conditions. In the last section, we give two examples of N(k)-mixed generalized quasi-Einstein manifolds.
Some classes of Lorentzian α-Sasakian manifolds with respect to quarter-symmetric metric connection
Tbilisi Mathematical Journal
The object of the present paper is to study a quarter-symmetric metric connection in a Lorentzian... more The object of the present paper is to study a quarter-symmetric metric connection in a Lorentzian α-Sasakian manifold. We study some curvature properties of Lorentzian α-Sasakian manifold with respect to quarter-symmetric metric connection. We investigate quasi-projectively at, ϕ-symmetric, ϕ-projectively at Lorentzian α-Sasakian manifolds with respect to quartersymmetric metric connection. We also discuss Lorentzian α-Sasakian manifold admitting quarter-symmetric metric connection satisfying P̃.S̃ = 0, where P̃ denote the projective curvature tensor with respect to quarter-symmetric metric connection.
Acta Universitatis Sapientiae, Mathematica, 2016
Quasi-Einstein manifold and generalized quasi-Einstein manifold are the generalizations of Einste... more 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 define 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.
On semi pseudo symmetric and semi pseudo Ricci symmetric Lorentzian para Sasakian manifold
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Some Types of Weakly Symmetric Riemannian Manifolds
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Pseudo projectively flat manifolds satisfying certain condition on the Ricci tensor
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In the present paper we study first the behavior of Ricci flow on Riemannian manifold satisfying ... more In the present paper we study first the behavior of Ricci flow on Riemannian manifold satisfying certain condition on the Ricci tensor. Then we study the uniform boundedness of R(x, t) and |∇f (x, t)| and using maximum principle we obtain uniform boundedness of f (x, t), where f (x, t) = −logφ(x, t) and the metric g(x, t) = φ(x, t)g E , g E being the standard Euclidean metric on n. Then we study the behavior of scalar curvature, Riemannian curvature tensor and Weyl tensor on η-Einstein manifolds under Ricci flow. Next we study the volume form of different type of manifolds under Ricci flow. We have also obtained the value of k on N (k)-contact η-Einstein manifold (k = 0) using critical points under gradient Ricci soliton. Finally we study the eigenvalues of symmetric endomorphism Q on a special type of trans-Sasakian manifold and on LP-Sasakian manifold satisfying certain condition under gradient Ricci soliton.
On Generalized Quasi-Kenmotsu Manifolds
On generalised Ricci-recurrent Kenmotsu manifolds
Semi-symmetric metric connection on a 3-dimensional trans-Sasakian manifold
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On some types of quasi Einstein, generalized quasi Einstein and super quasi Einstein manifolds
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Characterization on mixed super quasi-Einstein manifold
Tbilisi Mathematical Journal, 2015
In this paper we study characterizations of odd and even dimensional mixed super quasi- Einstein ... more In this paper we study characterizations of odd and even dimensional mixed super quasi- Einstein manifold and we give three and four dimensional examples (both Riemannian and Lorentzian) of mixed super quasi-Einstein manifold to show the existence of such manifold. Also in the last section we give the examples of warped product on mixed super quasi-Einstein manifold.
Some global properties of mixed super quasi-Einstein manifolds
Within the framework of mixed super quasi-Einstein mani- folds, are proved three theorems: the fl... more Within the framework of mixed super quasi-Einstein mani- folds, are proved three theorems: the flrst one shows that the compact orientable manifolds MS(QE)n (n ‚ 3) without boundary do not admit non-isometric conformal vector flelds, the second one provides a su-ciency condition for non-existence of nontrivial Killing vector flelds, and the last one characterizes the harmonic vector flelds under certain
IOSR Journal of Mathematics, 2014
In this paper we have found that if a Kenmotsu manifold with a Killing vector field satisfies gra... more In this paper we have found that if a Kenmotsu manifold with a Killing vector field satisfies gradient Ricci soliton equation then the smooth function is either constant or is orthogonal to the Killing vector field.
Annals of the Alexandru Ioan Cuza University - Mathematics, 2015
In this paper we have established some curvature identities for gradient shrinking conformal Ricc... more In this paper we have established some curvature identities for gradient shrinking conformal Ricci soliton.
In this paper, mixed super quasi-Einstein manifolds (MS(QE)n) have been deflned. The existence th... more In this paper, mixed super quasi-Einstein manifolds (MS(QE)n) have been deflned. The existence theorem and an example have been pro- vided and the relations between the associated scalars have been estab- lished. As well, manifolds of mixed super quasi-constant curvature are deflned, and it is shown that quasi conformally ∞at, conformally ∞at, con- harmonically ∞at and projectively ∞at MS(QEn) are
Volume Of A Tetrahedron Revisited
Demonstratio Mathematica, 2014
The volume of a tetrahedron is represented in terms of the twelve face angles, inradii of the fac... more The volume of a tetrahedron is represented in terms of the twelve face angles, inradii of the faces of tetrahedron, circumradii of the faces and the radius of the sphere circumscribing the tetrahedron
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Papers by Arindam Bhattacharyya