Parametric Equations of Geodesic and Magnetic Surfaces in three DimensionalHeisenberg Group

Abstract

In this paper, we extend the concept of a magnetic curve, which is viewed as a one-dimensional manifold representing the trajectory of a charged particle moving under the action of a magnetic field, to a magnetic surface considered as a two-dimensional manifold. For this purpose, we investigate the contact geometry of Heisenberg three-group denoted by H3. Subsequently, we determine the parametric equations of geodesic surfaces, which can be interpreted as magnetic surfaces in the absence of a magnetic field, and of magnetic surfaces. Lastly, we conclude with illustrative examples of such surfaces in H3 with graphical presentation in R3.