# For coordinates (left(x^{1}, x^{2} ight)) and metric (g=operatorname{diag}left(g_{11}, g_{22} ight)), the Gaussian curvature is For a sphere

## Question:

For coordinates \(\left(x^{1}, x^{2}\right)\) and metric \(g=\operatorname{diag}\left(g_{11}, g_{22}\right)\), the Gaussian curvature is

For a sphere with coordinates defined in the following figure,

show that a Gaussian curvature \(K=R^{-2}\) is obtained using spherical coordinates \(\left(x^{1}, x^{2}\right)=(S, \phi)\) or cylindrical coordinates \(\left(x^{1}, x^{2}\right)=(r, \phi) .

Fantastic news! We've Found the answer you've been seeking!

## Step by Step Answer:

**Related Book For**

## Symmetry Broken Symmetry And Topology In Modern Physics A First Course

**ISBN:** 9781316518618

1st Edition

**Authors:** Mike Guidry, Yang Sun