I started thinking about a situation in physics a while back and I once reached a situation where a force field was shaped so that there existed a surface $\mathcal S$ which had the property
$${\bf F}({\bf v}) \cdot {{\bf \hat n}({\bf v})} = 0, \hspace{1cm} \forall {\bf v} \in \mathcal S$$
Where ${\bf \hat n}({\bf v})$ was normal vector to this plane in the actual point.
The easiest way to realize such must exist is to take two equally massive planets, their forcefield will be symmetric and in the middle there shall be a plane which has the property that for any point in this plane, it accelerates stuff towards the center of mass of the whole system (which lies in the plane). So we could for example create orbits in this plane which are around an invisible point in the middle between the planets.
What would we call a surface like this? I suppose it has some name in physics?
(I throw in algebra tag because I suspect maybe we can view action of gravitation on a small object in this surface as a group in some sense. At least in plane case it is obvious that any motion starting in the surface will stay so we have a set with closure and should be possible to prove other group axioms as well.)