Timeline for eigenvalues of a Möbius strip

6 events

when toggle format	what		by	license	comment
Oct 1, 2014 at 16:17	history	edited	David E Speyer	CC BY-SA 3.0	added 2 characters in body
Oct 1, 2014 at 14:10	comment	added	AndyF		There appears to be a slight problem with the final part of David Speyer's answer: Pass to the double cover, which is a cylinder: [0,1]×[0,2] with the end points of the second interval identified. On the cylinder, the eigenfunctions are f(x,y)=sin(axπ)e^{ibyπ} with a and b integers and λ=−a^2−b^2. An eigenfunction descends to the Mobius strip if and only if f(x,y)=f(1−x,y+1) which means that a+b is odd. It makes sense (to me) that the conditions on the x/y directions (i.e. on a and b) should be coupled, otherwise I assume the double cover would be unnecessary...
Feb 28, 2011 at 15:56	history	edited	David E Speyer	CC BY-SA 2.5	added 1 characters in body; edited body
Feb 22, 2011 at 21:26	comment	added	Willie Wong		and perhaps you meant $f(x,y) = \sin(\pi a x) e^{i\pi b y}$?
Feb 22, 2011 at 21:24	comment	added	Willie Wong		um, why $f(x,y) = f(-x, y+1)$? Should it be $f(x,y) = f(1-x, y+1)$? In particular, is $a = 1, b = 0$ not an eigenfunction on the Moebius strip?
Feb 22, 2011 at 17:09	history	answered	David E Speyer	CC BY-SA 2.5