Sampa Pahan

Bio: Sampa Pahan is an academic researcher from Jadavpur University. The author has contributed to research in topics: Einstein manifold & Einstein. The author has an hindex of 4, co-authored 13 publications receiving 30 citations.

Geometry of conformal η-Ricci solitons and conformal η-Ricci almost solitons on paracontact geometry

Abstract: Abstract We prove that if an η \eta -Einstein para-Kenmotsu manifold admits a conformal η \eta -Ricci soliton then it is Einstein. Next, we proved that a para-Kenmotsu metric as a conformal η \eta -Ricci soliton is Einstein if its potential vector field V V is infinitesimal paracontact transformation or collinear with the Reeb vector field. Furthermore, we prove that if a para-Kenmotsu manifold admits a gradient conformal η \eta -Ricci almost soliton and the Reeb vector field leaves the scalar curvature invariant then it is Einstein. We also construct an example of para-Kenmotsu manifold that admits conformal η \eta -Ricci soliton and satisfy our results. We also have studied conformal η \eta -Ricci soliton in three-dimensional para-cosymplectic manifolds.

On Einstein Warped Products with a Quarter-Symmetric Connection

Abstract: 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.

On Ricci flat warped products with a quarter-symmetric connection

Abstract: In this paper, we have 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). dimM = 2, (2). dimM = 3, (3). \({dim M \geq 4}\)] and all the fibers are Ricci flat.

Multiply warped products quasi-Einstein manifolds with quarter-symmetric connection

Abstract: 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 Quasi-Einstein Manifolds Which Are Not Einstein

Abstract: A Riemannian manifold (M,g) is called a quasi Einstein manifold if for any coordinate system in M, its Ricci tensor S satisfes S_(ij) = ag_(ij) + bA_iA_j for some scalars a and b, where A(X)=g(X, p) for some unit vector p. This class of manifolds is a generalization of Einstein manifolds which are quasi Einstein manifolds whose b=0. In this paper, we will give examples of these manifolds and we will show that on each coordinate system, a and b are unique.

Timelike Circular Surfaces and Singularities in Minkowski 3-Space

Abstract: The present paper is focused on time-like circular surfaces and singularities in Minkowski 3-space. The timelike circular surface with a constant radius could be swept out by moving a Lorentzian circle with its center while following a non-lightlike curve called the spine curve. In the present study, we have parameterized timelike circular surfaces and examined their geometric properties, such as singularities and striction curves, corresponding with those of ruled surfaces. After that, a different kind of timelike circular surface was determined and named the timelike roller coaster surface. Meanwhile, we support the results of this work with some examples.

One-Parameter Lorentzian Dual Spherical Movements and Invariants of the Axodes

Abstract: E. Study map is one of the most basic and powerful mathematical tools to study lines in line geometry, it has symmetry property. In this paper, based on the E. Study map, clear expressions were developed for the differential properties of one-parameter Lorentzian dual spherical movements that are coordinate systems independent. This eliminates the requirement of demanding coordinates transformations necessary in the determination of the canonical systems. With the proposed technique, new proofs for Euler–Savary, and Disteli’s formulae were derived.

The Characterizations of Parallel q-Equidistant Ruled Surfaces

Abstract: In this paper, parallel q-equidistant ruled surfaces are defined such that the binormal vectors of given two differentiable curves are parallel along the striction curves of their corresponding binormal ruled surfaces, and the distance between the asymptotic planes is constant at proper points, which is related to symmetry. The characterizations and some other useful relations are drawn for these surfaces as well. If the surfaces are considered to be closed, then the integral invariants such as the pitch, the angle of the pitch, and the drall of them are given. Finally, some examples are presented to indicate that the distance between the proper points on the corresponding asymptotic planes is always constant.