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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?

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

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