How, if at all, would differential geometry differ between the opposite "sides" of the surface in question. Simplest example: suppose you look at vectors etc on the outside of a sphere as opposed to the inside. Or a flat plane? Wouldn't one of the coordinates be essentially a mirror while...
Does anyone know what the metric tensor looks like for a 2 dimensional sphere (surface of the sphere)?
I know that it's coordinate dependent, so suppose you have two coordinates: with one being like "latitude", 0 at the bottom pole, and 2R at the northern pole, and the other being like...
I would like to explore writing differential geometry in matrix format and was wondering if any of the experts here knows a good resource for that? I have tried Google and can't find anything definitive.
Thanks in advance!