Möbius band

immersion via f: the domain of f:D→ is a subset D⊂ around 0

The metric tensor g on D⊂ is the pullback of the standard metric tensor Id[3] on via f.

The following expression is the (euclidean) length of "going once around". The length is minimal "walking in the middle", i.e. when =0. In this case, the length is simply 2, the circumferrence of a circle.

Have a look at the standard tensors of the sphere: g, Γ, R, Ric, S

For some reason the following line takes forever to execute. In the next line we introduce a new coordinate , which parametrizes the local normal vector field.

Created by Mathematica (December 22, 2006) |