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

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William Elliot

Posts: 1,600
Registered: 1/8/12
Re: Surface geodesics
Posted: Jan 20, 2014 2:41 AM
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On Sun, 19 Jan 2014, ?~B?XPOSITO wrote:

> 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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