I have seen in many contexts that Euclidean geometry is called also "parabolic geometry".
As in many things in mathematics (conics, differential equations, algebraic equations) the terms: elliptical, parabolic, and hyperbolic refer to the conics with their corresponding names.
You could say that a plane is deformed paraboloid (can you?), but why is it that it is not important to consider geometry over a paraboloid?
I know Riemannian geometry considers geometry over general surfaces (manifolds) but there might be something uninteresting about parabolids that mathematicians do not like. What is it?
Thanks.
