A new construction on the energy of space curves in unit vector fields in Minkowski space E₂⁴

In this paper, we firstly introduce kinematics properties of a moving particle lying in Minkowski space E₂⁴. We assume that particles corresponds to different type of space curves such that they are characterized by Frenet frame equations. Guided by these, we present geometrical understanding of an energy and pseudo angle on the particle in each Frenet vector fields depending on the particle corresponds to a spacelike, timelike or lightlike curve in E₂⁴. Then we also determine the bending elastic energy functional for the same particle in E₂⁴ by assuming the particle has a bending feature of elastica. Finally, we prove that bending energy formula can be represented by the energy on the particle in each Frenet vector field.

Existence of some classes of N(k)-quasi Einstein manifolds

The object of the present paper is to study some classes of N(k)-quasi Einstein manifolds. The existence of such manifolds are proved by giving non-trivial physical and geometrical examples. It is also proved that the characteristic vector field of the manifold is killing as well as parallel unit vector fields under certain curvaturerestrictions.