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The map from a Surface to its Unitary normal vector field, when expressed as points on a Sphere

Differential of Gauss map

More generally, For a K dimensional manifold M embedded in R N , the Gauss map (Fig. 4B) maps a point  2 M to its K dimensional tangent plane TM 2 GK;N, where GK;N is the Grassmannian manifold of all K dimensional subspaces in R N