- #1

snoopies622

- 846

- 28

x= r cos(theta)

y= r sin(theta)

z= r^2

but in every case the Christoffel symbols have failed. For example, using the above, the basis vectors are

e sub r = < cos(theta), sin<theta>, 2r >

e sub theta= <-r sin(theta), r cos(theta), 0 >

and the partial derivative of e sub r (for example) with respect to r = <0,0,2>. Yet there is no linear combination of these two basis vectors that will make <0,0,2>. The other two coordinate systems I've tried have had similar difficulties.

A paraboloid strikes me as a legitimate 2-dimensional manifold. What am I doing wrong?