Consider a smooth embedding \(\iota\colon S \hookrightarrow M\). Why we ask \(\iota\) to be an immersion? I think it ensures that the tangent space \(T_pS\) can be embedded to \(T_pM\), since \(d\iota_p\) is injective by definition.
Consider a smooth embedding \(\iota\colon S \hookrightarrow M\). Why we ask \(\iota\) to be an immersion? I think it ensures that the tangent space \(T_pS\) can be embedded to \(T_pM\), since \(d\iota_p\) is injective by definition.