# Why constant metric tensor allows finite displacement

Consider as space coordinates $$q_1,q_2,q_3$$ why if the metric tensor is not constant in space $$q_1, q_2, q_3$$ can't be considered a displacement vector? And why vice versa, a constant metric tensor in space allows $$q_1, q_2, q_3$$ to be considered as a displacement vector?

• you mean that the metric tensor is not constant in space $\dfrac{\partial G}{\partial t}\neq 0$ ? – Eli May 16 at 14:14
• I mean $G=G(q_1,q_2,q_3)$ – SimoBartz May 16 at 14:30