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Topic: Surface geodesics
Replies: 16   Last Post: Jan 23, 2014 7:01 AM

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William Elliot

Posts: 1,238
Registered: 1/8/12
Re: Surface geodesics
Posted: Jan 20, 2014 3:31 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

On Mon, 20 Jan 2014, ?~B?XPOSITO wrote:

> Thanks a lot for your reply. I haven't yet thought about it, but I would like
> to ask you, if this is not a silly question, what are the symbols \/ and R.


\/ union; /\ intersection;
R the set of reals ordered by magnitude with the open interval topology.

Another example is a tube with it's axis bent into a helix.

> > > Can somebody provide an example of a connected surface containing a
> > > non-plane> geodesic, apart from those surfaces contained in the plane
> > > or the sphere? Does such a surface even exist?

> >
> > Yes.
> > ( (x,y,z} | x^2 + y^2 = 1, z in [-1,1] }
> > . . \/ Rx[-2,2]x{1} \/ [-2,2]xRx{-1}
> > . . - { (x,y) | x^2 + y^2 < 1 }x{-1,1}.
> >
> > A ribbon 3 ft by 4 in. twisted lengthwise 2 rotations.
> >
> >
> >

>



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