Recent content by Ogai

Further to the present thread, here is a link to a thesis which treats the same theme, i.e. "Locally Euclidean Möbius Strips" embedded in R3 and classified. It is also more recent than G. Schwarz's paper referred above in this thread...

Looks like I will have 'my' Möbius Strip as soon as I get the paper worked out. Thank you so much Hyper.

Please notice that a Möbius strip has only ONE single edge and not two. It is true that if you get two Mobius strips one twisted clockwise and the other anti-clockwise and you glue them along their borders you get a Klein bottle but that cannot be done in R3 without self-intersection. Yes, the...

Yes, your Möbius Strip is a sound one. Unfortunately it doesn't qualify, because its curvature is not zero. The sole component of the Riemann tensor for your example is R1212 = 16 / [s^2+4*(2 + s*cos(t/2))^2] which is not even constant and much less zero. The nature of the problem was to find...

I would welcome the parametric equations for an embedding in R3 of a locally Euclidean Möbius Strip without self intersections nor singularities and of Gaussian curvature equal to zero. That it exists in R3 is trivial to prove: just get a strip of paper of appropriate length and width, twist and...