(given that the ”manifold” in question is quite boring as there is a global chart, you could almost certainly make some sort of link to changes of variables. See, for instance, the two ways of turning an isotropic random field into a non-isotropic one: you can either define it on an explicitly deformed space and map it back to R^2 [Samson and Guttorp] or you can intrinsically define a metric through a spatially varying 2×2 positive definite matrix [Lindgren, Rue, LindstrÃ¶m])

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