Differential Geometry, orthogonal frames in R3, 1-27-21, part 3

[azziahmed]

thank you, we need to make video of frame and coframe in Heisenberg space

[AndrewLi]

Hi Prof. Cook, thanks for uploading the lectures! I'm still a bit confused about relating the cross and dot products to the corresponding differential form. While I understand that the terms are isomorphic, I have difficulty rationalizing the physical picture of the multiplication of partial derivatives to generate new partial derivative in the case for the cross product, and to a Kronecker delta for the dot product. Is there a more intuitive/physical picture for this, or a reference that you would recommend?