> [!theorem] > > Let $(X, g)$ be a $C^p$-[[Riemannian Manifold|Riemannian manifold]]. Define the map > $ > \wh g: TM \to T^*M \quad v \mapsto \angles{\cdot, v}_{g} > $ > from the [[Tangent Bundle|tangent bundle]] to the [[Cotangent Bundle|cotangent bundle]], then $\wh g$ is a $C^{p - 1}$-[[VB-Morphism|VB-isomorphism]].