- #1
quasar_4
- 290
- 0
I understand that we could think of a null curve in Minkowski space as being the curve c(s) such that the tangent vector dc(s)/ds = 0 at all s.
So suppose that we have a curve c(s) = (t(s), x(s), y(s), z(s)) and we want to ask ourselves what conditions would make c a straight line. I guess I'm having trouble understanding how c(s) as a straight line relates to tangency, if at all. Certainly one can think of a tangent vector at s as an equivalence class of curves passing through s, but I am not sure that's helpful.
Can anyone clarify this a bit?
So suppose that we have a curve c(s) = (t(s), x(s), y(s), z(s)) and we want to ask ourselves what conditions would make c a straight line. I guess I'm having trouble understanding how c(s) as a straight line relates to tangency, if at all. Certainly one can think of a tangent vector at s as an equivalence class of curves passing through s, but I am not sure that's helpful.
Can anyone clarify this a bit?