- #1
raopeng
- 86
- 0
In my geometry textbook it is stated that intuitively we can choose a suitable basis of coordinates that the components Christoffel symbol vanishes locally at that point(= 0). However can one obtain a formal proof of it? For example if we use rectification theorem to rectify the geodesics passing through a point into straight lines, can we say under such diffeomorphism the Christoffel symbol vanishes since the geodesic is mapped into a line in the neighbourhood of that point?