- #1
thehangedman
- 69
- 2
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 longitude, 0 on 1 meridian and Pi * R on the opposite side (here, 2 Pi R gives you the same location as 0).
I've searched online and can't find a simple example of this basic metric tensor... :-(
The other one I'm curious about is the surface of a hyperbola (again, think 2-D surface of a shape in 3 dimensions). What is the metric on THAT surface?
Any type of help is greatly appreciated...
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 longitude, 0 on 1 meridian and Pi * R on the opposite side (here, 2 Pi R gives you the same location as 0).
I've searched online and can't find a simple example of this basic metric tensor... :-(
The other one I'm curious about is the surface of a hyperbola (again, think 2-D surface of a shape in 3 dimensions). What is the metric on THAT surface?
Any type of help is greatly appreciated...