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## Main Question or Discussion Point

Hi,

Is it true to say on a topological manifold one can always find a unique metric such that a set of non intersecting curves become its geodesics? Is there any way to find that metric?

Thanks, Owzhan

Is it true to say on a topological manifold one can always find a unique metric such that a set of non intersecting curves become its geodesics? Is there any way to find that metric?

Thanks, Owzhan