Trying to use the straight arrow vectors of flat space in curved spacetime isn't possible. Analysis must start locally! So we build a tangent vector space to refine the definition of vectors into a local one, instead of the bi-local arrows (a point for the tip and a point for the tail).
This video is part of the mathematical prequisities for general relativity. The series is heavily influenced by Prof. Schuller's legendary lecture series on Gravity and Light, with my own insights added when applicable. See the playlist on: [ Ссылка ]_
The concepts of this video are discussed on: [ Ссылка ]
