Cartan's equivalence method

In mathematics, Cartan's equivalence method is a technique in differential geometry for determining whether two geometrical structures are the same up to a diffeomorphism. For example, if M and N are two Riemannian manifolds with metrics g and h, respectively, when is there a diffeomorphism ϕ : M → N {\displaystyle \phi :M\rightarrow N} such that ϕ ∗ h = g {\displaystyle \phi ^{*}h=g} ?

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