I believe that when people talk about N-dimensional spaces they typically talk about spaces with a Euclidean metric unless they explicitly say otherwise. The pr

I believe that when people talk about N-dimensional spaces they typically talk about spaces with a Euclidean metric unless they explicitly say otherwise. The properties of a sphere in an N-dimensional Euclidean space are not all the same as those in an N-dimensional Minkowski-like spacetime (either 6+1 or 4+3 or any combination).