Example 5.9.1. Let us take image and we introduce the spherical coordinates (r, θ, ø) connected to Cartesian coordinates by the relations

image

Since the arc element is determined by

image

the components of the metric tensor and its inverse are given by

image

Thus the volume form becomes

whence we produce the basis for

We can now represent a form by

where coefficients ...

Get Exterior Analysis now with O’Reilly online learning.

O’Reilly members experience live online training, plus books, videos, and digital content from 200+ publishers.