Lab

# Absos Ali Shaikh's Lab

Institution: University of Burdwan

Department: Department of Mathematics

# Featured projects (1)

The goal of this project is to investigate the topological and geometrical behavior of Ricci flow in a Riemannian manifold. Moreover, some more generalized notions of curvature flow are to be introduced along with their geometrical properties.

# Featured research (3)

Berger asked the question
"To what extent the preperiodic points of a stable p-adic power series determines a stable p-adic dynamical system ?"
In this work we have applied the preperiodic points of a stable p-adic power series in order to determine the corresponding stable p-adic dynamical system.

The motive of the current article is to study and characterize the geometrical and physical competency of the conharmonic curvature inheritance (Conh CI) symmetry in spacetime. We have established the condition for its relationship with both conformal motion and conharmonic motion in general and Einstein spacetime. From the investigation of the kinematical and dynamical properties of the conformal Killing vector (CKV) with the Conh CI vector admitted by spacetime, it is found that they are quite physically applicable in the theory of general relativity. We obtain results on the symmetry inheritance for physical quantities (μ,p,ui,σij,η,qi ) of the stress-energy tensor in imperfect fluid, perfect fluid and anisotropic fluid spacetimes. Finally, we prove that the conharmonic curvature tensor of a perfect fluid spacetime will be divergence-free when a Conh CI vector is also a CKV.

The main aim of this paper is to investigate the nature of invariancy of rectifying curve under conformal transformation and obtain a sufficient condition for which such a curve remains conformally invariant. It is shown that the normal component and the geodesic curvature of the rectifying curve is homothetic invariant.

# Lab head

Department

- Department of Mathematics

About Absos Ali Shaikh

- Differential geometry, Geometric Analysis, Non-Archimedean Geometry, Complex Differential Geometry, Hyperbolic Geometry, Geometry over Finite Fields, Gravitational Theory, Mathematical Modelling. Geometry of Curves and Surfaces.