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 $\dfrac{\partial G}{\partial t}\neq 0$ ? $\endgroup$– EliCommented May 16, 2021 at 14:14
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$\begingroup$ I mean $G=G(q_1,q_2,q_3)$ $\endgroup$– SimoBartzCommented May 16, 2021 at 14:30
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