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Riemannian Geometry is a subfield of Differential Geometry, which specifically studies "Riemannian Manifolds", manifolds with "Riemannian Metrics", which means that they are equipped with continuous inner products.

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Describe all differentiable functions on $\mathbb{S}^n \backslash S$ (S is the south pole)

I understand that one must prove that every smooth function $g : \mathbb S^n\setminus \{S\} \to \mathbb R$ can be expressed as $g = G \circ h$ where $G : U \to \mathbb R$ is a smooth function on some …
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