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1. A Opposite "sides" of a surface - Differential Geometry.

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...
2. Metric Tensor for a Sphere

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...
3. Matrix Formalism of Differential Geometry

Yes. The metric tensor would become a 4x4 hermitian matrix.
4. Matrix Formalism of Differential Geometry

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!