ABSTRACT
In this chapter, we outline several further applications of differential forms.
20.1 THE EQUIVALENCE PROBLEM It is easy to see that the line elements
ds2 = dx2 + dy2, (20.1)
ds2 = dr2 + r2 dφ2 (20.2)
are equivalent; both represent flat Euclidean space, the first in rectangu-
lar coordinates and the second in polar coordinates. What does equivalent
mean? That there exists a coordinate transformation taking one line ele-
ment to another, in this case the standard transformation between rectan-
gular and polar coordinates.
