perturbated core curve

the core curve of the mobius strip perturbated by  

But if we use

 

 

 

four geodesics in the band

on the right of this post you can see 4 (approximately) geodesics in the mobius strip, one is transversal to the core curve and the others (three)  begin at that transversal… One almost can see that all geodesics in the surface have curvature but without 3d torsion… would it be a theorem?  

Rendered with Mathematica-6.

a GPS for a surface to do calculus on it

 

torus in chains

more than thousand googolplex parole