Let g : M1 → M2 be a differentiable map between the differentiable manifolds M1, M2 of dimension l, m, respectively. The linear map which with every v ∈ TpM1, defined by v = ˙γ(0), associates w ∈...

Let g : M1 → M2 be a differentiable map between the differentiable manifolds M1, M2 of dimension l, m, respectively. The linear map which with every v ∈ TpM1, defined by v = ˙γ(0), associates w ∈ Tg(p)M2, defined by w = β˙(0), with β = g ◦ γ, is the differential dgp : TpM1 → Tg(p)M2.