Resumen de Translation curves and their spheres in homogeneous geometries

Emil Molnar, Brigitta Szilagyi

• In this paper ve 3-dimensional homogeneous geometries Sol, Nil, and product geometries (H2, S2) are discussed.We introduce a seemingly new family of curves, called translation curves. These curves seem to be more natural in these geometries, than their geodesic lines. Visualization of the corresponding curves and spheres has also been elaborated