Unless you were breaking the speed of light at the time there by warping the planes.
Actually, mapping euclidean space to a moving frame near c would not make any difference here (see special relativity and Lorentz contraction).
However, near a gravitational field it would, which is the whole idea behind differential geometry and general relativity -- incorporating spacetime geometry into everything.
The thing is, since gravity goes as the inverse square of the distance, it never technically goes to zero, and thus the familiar geometries we're used to are actually only a special case of something much more complicated.
