Surfaces in \(\mathbb E^{3}\) making constant angle with Killing vector fields (Q2888821)

The authors study curves and surfaces which make a constant angle with a certain Killing vector field in the Euclidean space. Note that Killing vector fields in the 3-dimensional space are induced by translations or rotations or a combination of both.NEWLINENEWLINEIn the first part of the paper the authors completely classify the curves which make a constant angle with the Killing vector field \(-y \partial_x +x \partial y\). The class of curves obtained can be thought of as generalisations of the logarithmic spiral in the plane.NEWLINENEWLINEThey also treat surfaces which make a constant angle with this vector field. In that case, the solution is either part of a plane, a rotational surface, a cylinder over a logarithmic spiral or the well known Dini's surface.